I am trying to take save files from a game of Fallout2 on my desktop with me on my laptop, but I can't figure out where the files are saving. Does anyone know what I need to transfer so I can play my saved games from my desktop on my laptop?

Yeah, that's where I thought it would be too, but since I installed GOG"s version, its in the GOG folder. Ok, no problem. But then when I look in the data folder, no SAVEGAME file. Anyone who downloaded the GOG version know where it puts SAVEGAME?

Well the gog version may have it installing to your documents folder on xp or your user profile on vista.
On xp check
C:\documents and settings\(your username)\aplication data
or
C:\documents and settings\(your username)\local settings\aplication data
The folders may be hidden so if they are go to tools(across the top), folder options, view tab then where is says hidden files and folders change that to show them.
For vista check
C:\Users\<Username>\Documents\My Games

If they're not in the install folder or the my documents folder, it might be the old vista 'relocating non-admin data' trick (assuming you have vista). Have a look in
C:\ Users \ <username> \ AppData \ Local \ VirtualStore \ Program Files
and see if there's a fallout folder somewhere in there. App Data is a hidden folder by default.

My save data is located here: C:\Program Files\GOG.com\Fallout 2\data
I am using vista and when using another OS it may be different...

It's something to do with user account control, I THINK that if you have that turned off then the saves go where they're supposed to but if you have it on, it detects a non-core OS application is trying to act as an administrator and create files and sort of treats it like a virus & quarrantines it

i turned off UAC the first day I got vista, so that could be the problem. Occassionally a game will save its files to C:\Users\<username>\Saved Games. I hate it when it does because I can't find them, but no GOG have saved here for me.

I'm using XP and it IS in data folder, same directory as yours.

Files are redirected to VirtualStore on Vista and 7, but only when UAC is enabled (which is the default, and strongly recommended); if UAC is disabled or the program is running with admin elevation, files are stored in the real location. VirtualStore is preferable, however, as it means you can back up all your saves and settings simply by copying your user profile. On XP and earlier, backing up saves and settings was incredibly frustrating and time-consuming as every game had its own way of organising them.
GOG does not change the internal behaviour of the games being sold. Only newer games make use of the saves directory; this standard is encouraged by Microsoft and is a requirement of the Games for Windows brand, so in the future only non-compliant games will store files elsewhere.

Did you ever end up finding it?