migo: I've searched for this, and the solution is to edit the ut2004.ini file - something the GOG version is missing. Is there a way for me to set the resolution manually, preferably to 1920x1080 native, and if not, to a 16:9 resolution so the image isn't stretched?
korell: The GOG version is not missing the UT2004.ini file. In all likelihood, you've installed into a Program Files folder and are using Vista/7/8, meaning that Windows DEP forces the game to place the ini file elsewhere (along with settings and save files).
If this is the case then either uninstall and re-install into an unprotected folder such as C:\Games\UT2004\ or search for the ini file within your C:\Users\<Username>\AppData folder. Possibly it is inside Local\GOG.com but I'm not 100% on that. It could be in the VirtualStore folder, or some other place within AppData.
UPDATE: Ah, here we go. Checking the rest of the Unreal forum here is another post on this issue which I responded to, and the user located the file.
http://www.gog.com/forum/unreal_series/missing_ut2004_ini If you've installed into the Program Files folder (which is protected under Vista and later) then the ini file is located here:
C:\Users\<YOUR WINDOWS USERNAME>\AppData\Local\VirtualStore\Program Files\GOG.com\Unreal Tournament 2004\System
Thankyou, that did the trick. And I'm sure it'll help me for a lot of other games in the future.