What fixed it for me was using Timeslip's enhancement package (the ddraw.dll with the respective ini file). Make sure to try mode=0 (default, 8 bits) first, e.g., don't modify _any_ of the defaults. As soon as you tinker with the options, be prepared for strange results, though :)

Alright, I just finished downloading and installing Fallout from GOG. It says "Version 1.2" in the lower right corner of the title screen. Are there any patches I need or am I good to go as is?

you're good to go.

Quite true. I'd like to suggest the TeamX patch 1.3.4, though, as it fixes a plethora of bugs.

An easy fix for the 640x480 error message with the HiRes patch is to simply rename or delete the DDRAW.DLL in your Fallout folder. At least that fixed it for me and the HiRes patch is now working wonderfully on my MSI Wind Netbook.

This worked for me, as well.

thanks! I just bought and installed this game, and was having problems with the patch. This did the trick

I'd also like to suggest that if you're using the high-resolution mod you should also use Timeslip's mod for optimal performance. This may be obvious to some if not most users already, but these mods will support widescreen resolutions.

When I first installed Fallout I got rid of the ddraw.dll file for better performance and then installed the High-Res 1.3 mod without a problem. The game played great for a little bit until it started blacking out constantly. At first it wasn't too much of a problem as I could just keep moving my mouse to the edge of the screen to remove the black. But now it is becoming a real nuisance. Every 2 - 5 seconds my screen will black out and I have to move my mouse erratically like a toddler on guarana. I read around the GOG.com forums and followed a lot of advice including:
Installing Timeslip's engine fix.
Renaming either the new ddraw.dll file or falloutw.exe
Changing the settings of Timeslip's ddraw.dll
or even downright uninstalling the High-Res mod.
Unfortunately none of these worked. I don't know what to do and it is really, really annoying. The game is playable but not enjoyable if every few seconds I get interrupted by a blackout. Any help, advice, instructions I didn't follow, et cetera? Much appreciated. ^^
Edit: I realized what was causing the blackouts and it's simply renaming or removing the original ddraw.dll. If I were to replace it with anything else I would constantly blackout. Is there some way around this? The original ddraw.dll file makes the the game terribly slow and I can't play with it or without it... ='(
Edit 2: While nothing works for me I realized that simply letting the program run for an hour or so lessens the amount of black-outs to nearly zero. Also, starting a game from scratch produces nearly no blackouts until you exit and load a saved game. Then the blackouts become unbearable until you let the application run for a while. Really, really weird... O.o
Edit 3: And now the blackouts are completely gone. What a fickle game... Oh well, time to enjoy.

I have no experiencing with modding games, where and how do I insert the files?

Normally when you unzip the file(s) there is a readme inside that will instruct you on where to extract. There are also (normally) instructions on the website you're downloading the mod from. For Fallout 1 you simply extract all of your files to the directory you placed Fallout in (default is C:Program FilesGOG.comFallout). Windows XP and Vista come with a default file extractor but if you want something a bit better download Winzip or WinRAR or 7zip (do a Google search for these) and install them. Once you have done so and downloaded the mod open it up and look for the "extract" button. When you find it, click on it and input your Fallout 1 directory. It should place the mod files into the Fallout 1 folder and modify the game. Voila.
This doubles for most games. Some mods come with installers that you just open and run. ^_^

So all I have to do is take the files from the mod folder and put them into the Fallout folder? Or is there a specific spot inside the folder?

Ok, I got it to work and it seems like everything is ok. The only issue is that when I start it, all the colors are really crazy. There are greens and reds and other weird colors where the should not be. Does this happen to everyone?

I simply restarted the game and the inverted colors went away. I never had it more than once. Take a peak at this thread: http://www.gog.com/en/forum/Fallout_Series/fallout_2_colors_problem/30

I'm having trouble getting Falche to work as well. I unzipped it, pointed it to my Fallout folder, found the character slots and edited the file a bit, but when loading up the game it does not reflect the changes. What did you do to fix it? Is anyone else having similar problems?