The best answer is: it depends.
If your game is running in full-screen mode, then usually the answer is no, it won't work. This is because the full-screen mode of the game blacks out all other windows.
However, if you run your game in a windowed mode, the answer is a resounding yes! Windows (both XP and Vista) will allow you to extend your desktop on to the second monitor, and you can then move windows from one screen to the other, or even have them span both screens.
Many games will give you the choice of running full screen or windowed. Flight Simulator X works perfectly this way. The second monitor can be used for instruments like the GPS, instrument panels, communications, etc., while keeping the main view clutter free.
On my dual-monitor system, I frequently have an internet browswer or word processing program open and maximized on one monitor, and several smaller apps on the other as I need them -- a Windows explorer window, calculator, etc.
To really enhance your dual monitors, check out the program UltraMon from Realtime Soft, available at http://www.realtimesoft.com/ultramon. This neat little program will add buttons to the top of your windows that, with one click, will move the window to the opposite monitor and maximize the window across both monitors. It even adds a second task bar to the bottom of your second monitor, so that each program appears on the taskbar on the screen in which it resides.