This should be pretty obvious, but you can get higher resolutions in TR1 by editing "glide.ini" in the "Tomb Raider 1 2 3\Tomb Raider 1" folder (there is another "glide.ini" in the "Tomb Raider 1 2 3\DOSBOX" folder, but that seems to be ignored) and changing the following line:
Resolution=0.0
to something like this:
Resolution=1024.0

EDIT: Just noticed I made a mistake before: the number stands for the width only, the height is computed automatically (always 4:3 it seems).

Can you get widescreen resolutions (even if stretched) like that?
Like:
1680.1050

No, it seems it has to be 4:3

Are the black bars that appear along the top and one side (like the game image has been moved into a corner) normal? I can't seem to get rid of them no matter what I change in the DOSbox or glide config. I'd like to play the game without the image stretch like i'm able to with other DOS games if possible.

If it has to be 4:3, than you must calculate the resolution.
1080p can be got by using: 1440x1080

Why this resolution? Well, 1920x1080 is 16:9, now you must calculate it to 4:3.
The source is the 1080p what you want to get:
1080 * 4 / 3 = 1440

I hope that this works with Tomb Raider. If not, 1024x768 should be enough. ;)

You could try messing with the settings in "dosboxTR.conf". I recommend changing fullresolution=Original to your native screen resolution, like fullresolution=1920x1200. If that does not help, try fullscreen=false to make the game run in a window.

Edit: And like Kyle07 above said, you should match the vertical resolution in glide.ini as closely as possible to 4/3 of the horizontal resolution of your display or whatever you set in dosboxTR.conf for fullresolution.

By changing fullresolution= to 0x0 in DOSbox and changing Resolution= to 1024.768 in glide I solved the black bars problem but the in game image still stretches. (i'm playing on a 16:10 monitor with a max res of 1440x900) The strange thing is that the logos at the start of the game keep the non-stretched resolution (which is what i'm trying to do for the game), but the title screen and in-game play are stretched. Are there any other combination of settings in DOSbox and glide I can try that would keep the gameplay from stretching?

Did you try setting fullresolution to your native resolution? If aspect=true in the same config file, the graphics should stay centered in a 4:3 aspect ratio.

If not then the glide wrapper somehow overrides DOSBox' video output (don't quite understand how this works), then your graphic card scaling options are probably to blame. On my ATI driver I find this option under "Properties (Built-in Display)" were I can select between "Full Screen", "Centered", and "Keep Aspect Ratio".

Tried that, no luck. Unfortunately my card and monitor can't do the "keep aspect ratio" thing, but that will be solved as I plan on getting a new PC eventually. Thanks for your help anyways.

As far as I can tell, the resolution in glide.ini is only meant to be the horizontal number, so you should put 1024.0 and it will automatically calculate the height.

It also says that any number less than 16 will be treated as a scaling factor. The original resolution appears to be 640x480, so I think if you put 1.6 for the resolution it should also give you 1024x768.

I have a 1920x1080 monitor and I had to fiddle with it to get the highest resolution I could which was still centered. I tried for the full 1080 vertical resolution but then it did the thing where the image is in the lower left of the screen instead of centered. I ended up putting 2.0 which gave me a resolution of 1280x960 centered in the middle of the screen with equal-sized bars on the left and right (and no bars on top or bottom).

I don't now what's wrong here, folks, but I had to edit "glide.ini" in the DOSBOX folder and "dosboxTR.conf" in the \Tomb Raider 1 folder, not the other way around.

I use a Nvidia 9500 GT and I don't get any black bars anywhere with fullscreen=true in dosboxTR.conf, so to be on the safe side I edited my file like this:

~\Tomb Raider 1+2+3\Tomb Raider 1\dosboxTR.conf
--------------
fullscreen=true
fullresolution=1680x1050
windowresolution=1680x1050

~\Tomb Raider 1+2+3\DOSBOX\glide ini
-----------------
Resolution=1400.0
InitFullScreen=1

1400 equals 1050 (my vertical screen res) /3*4 for the game's 4:3 aspect ratio. It seems arbitrary resolutions are supported. If you don't need to see the menu texts or the very bottom of the screen, you can set Resolution to 1680 and enjoy the game in fullscreen without widescreen distortion - in that case, leave InitFullScreen=0.

initFullScreen=1 scales the game from sort-of windowed 1400x1050 to fullscreen 1680x1050 and gets rid of my desktop and taskbar that remained visible - the game doesn't care what resolution or fullscreen settings I chose in DosBox, as long as they are larger than the glide settings. CreateWindow=1 doesn't seem to have any effect.

Your solution doesn't make it for me J0kun8u4ck (note that I have the same screen res as you)
Case 1 the game stays stuck on the left with a huge black bar on the right
Case 2 it simply crashes after the FMVs

EDIT : the highest resolution I can achieve without graphical fuck up is 1280*960
anything above gives me the evil black bar, including 1400*1050 (native screen res is 1680*1050)

Yes the game stays pinned at, and all scaling is done from the top left corner, but I don't get any black bars - most likely a driver issue (mine: Geforce 9500 GT/drivers v.301.42 under WinXP Sp3 32-bit).

I have some video issues with some FMVs, like the introductory movies (after you've started a new game) playing with sound and a black screen, but no crashes. The intro movie and logos work fine.

I'm now playing with resolution=1680 and initFullScreen=0 in glide.ini. The game is simply cropped from 4:3 to 16:10, so the bottom pixels where Lara's feet and the menu texts go is missing, but there's no widescreen stretching and the AR of 4:3 is maintained in the game. Also there's no needless scaling by DosBox involved.

So, how do you get higher resolutions?

This is what I get when I put Resolution=1920.0 in glide.ini:
http://i33.photobucket.com/albums/d94/soopytwist/TR1GOG_zps2b72acde.jpg