Ok this game is VERY old but you might want it for nostalgic reasons. It 'may' only work for single player, i haven't tried it online (version might be different). I searched online for a widescreen hack and couldn't find one so i downloaded the source and made my own (all perfectly legal - id released source code for Quake II). You can download the recompiled .exe here.
vidmode_t vid_modes[] =
{
{ "Mode 0: 640x480", 640, 480, 0 },
{ "Mode 1: 720x480", 720, 480, 1 },
{ "Mode 2: 864x480", 864, 480, 2 },
{ "Mode 3: 1280x720", 1280, 720, 3 },
{ "Mode 4: 1280x768", 1280, 768, 4 },
{ "Mode 5: 1280x800", 1280, 800, 5 },
{ "Mode 6: 1280x864", 1280, 864, 6 },
{ "Mode 7: 1280x1024", 1280, 1024, 7 },
{ "Mode 8: 1440x900", 1440, 900, 8 },
{ "Mode 9: 1680x1050", 1680, 1050, 9 },
{ "Mode 10: 1920x1080", 1920, 1080, 10 },
{ "Mode 11: 1920x1200", 1920, 1200, 11 }
};
These modes replace existing 4:3 modes. You probably already have an old mode set which will cause quake2 to open in a window after copying this exe. Set the new video mode and then you can go fullscreen by hitting ALT-ENTER. You can also set this mode in config.cfg in the baseq2 directory.
You may have to install the final quake2 patch from www.idsoftware.com for this exe to work right with other dlls. I'm not a quake2 programmer and hoped someone else had already done this, but i could not find this and knew this would be easy to add to the source code. Fortunately the source code provided by ID compiles with Visual Studio.NET 2K3 without any tweaking or i would have given up.