When playing older games, I usually try to play them as close as possible to the way they were when they were released. Especially with older 3D games, this can be a bit difficult. In the case of Doom, for example, there is the wonderful Chocolate Doom source port, which works with all modern machines but behaves and looks just like it did in 1993 on DOS.
With Quake that initially appeared to be a little more difficult, but I am very happy with the final results and wanted to share these for other afficionados of good old "chunky pixels" :)

GOG Quake already includes 3 different versions:
1. A DOSBox emulation of the original software rendered DOS release
2. The official OpenGL version GLQuake
3. WinQuake, a windows port of the DOS version
There is a very good article about the differences between DOS and GLQuake here: https://www.quaddicted.com/engines/software_vs_glquake
The article makes it clear that GLQuake is quite subpar compared to the DOS version. However, like fellow GOGers, I couldn't get Quake to work comfortably using DOSBox. As GOG provides it the performance is rather bad and only gets worse on higher resolutions. The Quake wiki suggests different settings: http://quake.wikia.com/wiki/DOSBox But even then I felt the controls are very sluggish and it just isn't much fun to play, despite the nice classic graphics.
WinQuake on the other hand is nearly identical to the DOS version in look and feel, while working flawlessly on my modern machine, albeit with a slightly washed out look due to being brighter and less contrasted. Still, that is a great choice if all you want is to play the original Quake without any bells and whistles. However, there are more modern choices, all with different features:

Here are comparison screenshots between DOSBox, Winquake and 4 different source ports. All screenshots were taken in 640x480 but resized to 2x size:
DOSBox
WinQuake
FitzQuake Mark V WinQuake
FitzQuake Mark V WinQuake modified
Quakespasm
Quakespasm modified
DirectQ
engoo

and the source ports in 1920x1080:
FitzQuake Mark V WinQuake
FitzQuake Mark V WinQuake modified
Quakespasm modified
DirectQ
engoo

The main "issues" with source ports, which of course are largely down to personal preference, usually are:
-texture filtering: As can be seen and described in the article, the DOS version looks crisper, but also noisier, whereas with linear filtering as in GLQuake, the textures look softer, but muddier
-particle effects: In the DOS version, every particle is shown as a simple square, in many source ports they are shown as rounded dots
-enemy animations: in the DOS version animations are made up of only few frames, making them look very choppy. In most source ports the animations are interpolated, resulting in a much more fluid animation
-weapon placement: Depending on the rendering and also resolution, the weapon placement on the bottom of the screen can be pretty different, as is obvious in the screenshots
-brightness/contrast: The DOSBox version looks dark and contrasted. Most source ports, including WinQuake, appear less vibrant, even on the lowest brightness settings. However, this can easily be changed by using the following command in the console (opened by pressing ~ or ^ on your keyboard):
gamma x (where "x" can be any number between 0.5 and 2. The default minimum is 1, higher numbers are even darker.)
and, if the source port includes it,
contrast x (I will give value recommendations per source port)

FitzQuake Mark V (WinQuake) (website)
Recent versions of this engine include a port based on WinQuake. It's nearly identical to that, while adding several features, like support for higher resolutions, MP3 music as well as the CD support, and lots of other features like weapon movement, while always clearly showing which option is the "default" original one. Brightness and contrast can be changed (I prefer gamma 1.2 and contrast 1.6), resulting in the look as shown in the "modified" screenshots.
Animation interpolation can be disabled by typing the following commands in the console (opened by pressing ~ or ^ ingame) or adding them to the autoexec file in the Quake/id1 folder (for example "C:\GOG Games\Quake\id1\autoexec.cfg". If it doesn't exist just create a new textfile and rename it to that):
r_lerpmove 0 (disables interpolation for enemies)
r_lerpmodels 0 (disables interpolation for everything else, for example weapons)

Quakespasm (website)
This seems to be the most popular source port. All issues are present here: Textures are filtered, particles are rounded, enemy animations interpolated and you see much less of the weapon. Luckily, despite not offering many options in the game's settings menu, most of these can be modified easily using the following command variables. Type them into the console or add them to autoexec.cfg as described above:
gl_texturemode 1 (disables texture filtering, 3 enables mipmapping resulting in less "noise" when moving)
r_particles 2 (changes to square particles)
r_lerpmove 0 (disables animation interpolation for enemies)
r_lerpmodels 0 (disables animation interpolation for everything else, e.g. weapons)

To my knowledge, the lower weapon placement can only be adressed by changing the "camera" placement, thus slightly altering the viewpoint, using this command:
scr_ofsx -2.8 (the value can be adjusted, although I found this the most suitable)

Brightness and contrast can be changed from the menu or using commands (I prefered gamma 1.2 and contrast 1.5).
All of this combined results in the look shown in the "Quakespasm modified" screenshots. If it weren't for the weapon placement it would be nearly identical to DOS/WinQuake.

DirectQ (download links, newest release is "DirectQ 1.9.0 Executable.zip")
Unlike Quakespasm, this source port uses Direct3D, so depending on your system you may get better performance using one or the other. It offers the most menu options out of the source ports I've tested, meaning you can easily adjust many variables to your liking, including brightness and contrast (I preferred gamma 0.6 and contrast 1.5 for the dark, vibrant look, but it doesn't show in the screenshots). Overall it feels slightly different to WinQuake but it's very close. To get closest to the orignal look, these settings need to be used in the video options:
Texture Filter: Point
Mipmap Filter: Off
and in the effects options:
Particles: Square
Animation interpolation can not be changed in the menu, but just as easily as in other ports by typing in a console variable or adding it to autoexec.cfg:
r_lerpframe 0 (disables animation interpolation)

Weapon placement in DirectQ is not identical, but fairly close to the original.

engoo (website)
This engine is based on the software-rendered WinQuake and thus, out of the box, looks and plays very similar, but not as close as Fitzquake Mark V. This one however is unique in that it offers a great number of extra options to mostly alter the look and feel, including color intensity, different presets allowing the game to mimick for example Quake64's look and much more. I can't recommend it for the orignial Quake feel, but this is good for a different kind of "retro"! Unfortunately, issues I have found are that it doesn't save resolution options until the next start, on higher resolutions the particle size is too big and apparently engoo doesn't play the original soundtrack in any way.

One important side note: Coloured lighting / Transparent water
Of the source ports mentioned here, FitzQuake Mark V (although not the WinQuake port!), Quakespasm, DirectQ and engoo support coloured lighting, which Quake originally didn't include. This is a big change, but depending on your opinion it can greatly enhance the atmosphere of the game. To benefit from that I recommend to use this pack of .lit and .vis files for Quake 1 and the addons provided by FitzQuake Mark V: http://quakeone.com/markv/extras/vis_lits_id1_hipnotic_rogue_free_standing_files.zip (simply extract the files into the corresponding maps folders)

All engines offer more and less slightly different experience, so it's really a matter of preference which one suits you best. After having tested several now the clear winner for me is the WinQuake port of FitzQuake Mark V. It looks, plays and feels exactly like the DOS version, runs flawlessly and plays the soundtrack without need for the CD!

I hope this topic is of some help for others. If you have any questions on using these engine or have any further advice I would be glad to hear it :)

Thanks! I agree, I am also focused on making Quake look and feel like the DOS version because it has the most "special" atmosphere. It just loses a lot of its appeal for me when softened with some modern techniques.

I have found out that it was a bit foolish to overlook WinQuake which GOG bundles with the other versions, as that's actually a very accurate port of the software rendered DOS version. I have added this and the source port "engoo" based on it to the opening post in favor of Ultimate Quake Engine.

[edit]
After having come across the excellent FitzQuake Mark V WinQuake port I have restructured the post a last time. Despite many guides and tons of source ports on the internet it has been a bit difficult finding the perfect setup to play Quake exactly as it was in 1996, but it's possible! Hopefully this makes it a bit easier for others in the same boat :)

Also a fan of pixels here. But since Dissolution of Eternity and Scourge of Armagon cannot be played in WinQuake I'm stuck with GLQuake. Do you have any idea how the resolution commands work?

I just gave it a try and could run both mission packs using WinQuake and Fitzquake Mark V Beta. For this you only need to create a shortcut to either Winquake.exe or mark_v_winquake.exe, right click on it, select "Properties" and under "Target" add "-game hipnotic" for Scourge of Armagon or "-game rogue" for Dissolution of Eternity. For example, the target section could look like this: This will run Scourge of Armagon using Fitzquake Mark V Beta.

If you really want to use GLQuake, which is not advisable as shown in the Quaddicted article mentioned above, it needs to be set similarly using command lines. "-width" and "-height" are used for the corresponding resolution, "-bpp" for the color depth, usually 16 or 32bits per pixel. So, if for example you want to play GLQuake in a resolution of 1280x1024 and 32bits color depth, the target section of the shortcut could look like this: Though, when I just tried this the game crashed. If you want to play Quake using OpenGL I would advise you to just use Quakespasm, otherwise try WinQuake or Fitzquake Mark V :)

After having played through Quake 1 using Fitzquake Mark V Winquake without any trouble, I now turned to Quakespasm again for mods. I investigated a bit more and found out that I was actually using the "wrong" texturemode. Using texturemode 1 (or "GL_NEAREST") actually fully disables texture filtering, thus resulting in a look very close to the DOS original. Quakespasm also now allows for changing the contrast so it appears less washed out.
Finally, I learned about the command line variable "scr_ofsx" with which you can change the placement of the "camera", moving it closer to the weapon. This is not an ideal way of circumventing the "faulty" placement in Quakespasm, but it definitely looks a bit better in my opinion. I've updated the original post accordingly and added new "Quakespasm modified" screenshots.

With all this combined I now think Quakespasm is actually a viable alternative for playing Quake close to what it originally looked like, although it's still clearly second to Fitzquake Mark V Winquake in my opinion.

[edit]
Oh boy, I was also a bit wrong about DirectQ's settings, as in this one you can also completely disable texture filtering. Updated the post again and added the info that coloured lighting is also supported by Quakespasm and DirectQ. If there's interest I might make some comparison screenshots to show off the coloured lighting.

[edit²]
Didn't want to make a new post: Fitzquake Mark V was just released as 1.0 and it includes the mentioned Winquake port, an OpenGL port and even a DirectX port as an alternative download. This is still a really good alternative to WinQuake and now even more versatile, worth a try :)

Having played around with a bunch of source ports I agree that WinQuake Mark V is the most authentic while still allowing music playback.

I have a constant annoying frame stutter/skip issue in Mark V WinQuake however. Do you know of any way to vsync this version?

I just had a quick look and you should be able to turn it on by just typing vid_vsync 1 in the console or changing said value in the config.cfg file in the "id1" folder.
I'm not running the latest version of Mark V Winquake right now, but it should apply to all versions :)
I hope it works for you!

There is no such command in WinQuake unfortunately. You must be thinking of regular Mark V Quake.

I had actually tried it in Mark V Winquake, but as I mentioned I was using an older build and, sure enough, the most recent release doesn't include the command anymore!
Still, I can recommend two things:
1) Tell the developer Baker about your problem here: http://celephais.net/board/view_thread.php?id=61375
That is the official development thread. Scroll down to the bottom and you can just write a message without registration, the developer himself or others are usually quick to answer. Maybe the command didn't work as intended or was thought to be obsolete, so any feedback should be appreciated. It could have also just been renamed, but I didn't find out anything.
2) Grab an older build that still includes "vid_vsync" from here and see if it works for you: http://quakeone.com/markv/builds/
Trying some out quickly it seemed that "1025_mark_v_beta.zip" from january is the last version to include it.

Hello, I know this is an old thread, but I think it makes sense for me to post this.
Syrion, your settings are great and I've been using them for awhile, but since I can't run fitzquake for some reason I play on quakespasm. Anyway, recently I watched a video by youtuber dwars where he talks about setting up quake to make it look chunky and vanilla on the quakespasm port. Here is the link to the steam page of this guide:
https://steamcommunity.com/sharedfiles/filedetails/?id=1427945447

Also, here is my own autoexec.cfg:

gl_texturemode "gl_nearest"
r_particles "2"
r_scale "2"
r_lerpmove "0"
r_lerpmodels "0"
r_viewmodel_quake "1"
gamma "1.3"
contrast "1.5"

The key option is r_viewmodel_quake 1!!! It makes the weapon placement look like vanilla quake.
I adjusted r_scale to taste, this one looks the best on my screen.
Also, I found gamma 1.3 and contrast 1.5 looked best on my screen.

The attached screenshot is with resolution set to 1280x960 and the above settings.

Edit: I added a new screen shot, resolution 640x480, r_scale is off, and gamma 1.2 contrast 1.6. This looks almost exactly the same as your fitzquake setup.

Thanks for your additions! I wonder if the command "r_viewmodel_quake 1" was only added in recent years, as I spent a lot of time in 2016 trying to get it right, but never came across it. Either way, it's great to have and it's good to know there are several options to play Quake 1 very smoothly but still totally "retro" :)

According to the quakespasm changelog, r_viewmodel_quake was added at the end of 2017, they noted it emulates the Mark V WinQuake weapon position. It really is great that there are many quality source ports continually being developed both to resemble vanilla Quake and to support the many creative community mods.

I know this is super old thread, but I was lost at how would I get those 'chunky pixels' in ANY game, for months.

You can use dgvoodoo2 to force any game to use Point Sampled texture filtering.

Sorry to necro, but Ironwail is starting to become another good soureport that can recreate the classic look of vanilla Quake and it is based off Quakespasm too but aims for performance over compatibility. It is still a WIP but it is still actively being developed, plus it also supports the 2021 remaster version's PAK files too.