spirithawk12: Cool, thanks for the info. I'm hoping that most games on GOG handle widescreen gracefully (especially the windows 95 and above stuff), but I have a feeling some wont.
Usually, you can set your graphics card to handle non-widescreen games by putting black bars on the sides. You do this by looking for "flat panel scaling options" or similar in your graphics card control panel. If you select "use scaling but maintain aspect ratio" then a non-widescreen game on a widescreen monitor will scale up to fill the screen but there will be black bars on the sides to the aspect ratio is still the same as the original game. There can be a few tricks you have to play with these settings sometimes, but usually you can get them to work.
EDIT: You will only need to set this for non-DOSBox games... as stated above, DOSBox has its own way of handling widescreen.
Also, for a surprising number of games it's possible to actually run them in widescreen. Sometimes this requires a fan-made patch, like the ones for Arcanum or Planescape: Torment. Other times you can simply use an .ini file edit to get a widescreen resolution with correct aspect ratio (and correct FOV for 3D games). A great place to learn about widescreen possibilities is the Widescreen Gaming Forum:
http://widescreengamingforum.com/
Just search for the game you're interested in and it will tell you how to set widescreen and how widescreen is handled; widening the horizontal view (HOR+), cropping the vertical view (VERT-) and stretching the image (stretch) are the most common. For example, here's the entry on enabling widescreen in Deus Ex, which uses HOR+ with a simple .ini file edit:
http://widescreengamingforum.com/forum/6272/deus-ex