I have seen several games that have a video display mode that is windowed with no borders, at the same resolution as the desktop. It's sometimes called "Borderless Windowed" mode, or "Maximized Fullscreen" mode. It seems to balance the trade-off between running in fullscreen, and running a game in windowed mode.
Fullscreen vs Windowed
A game in fullscreen mode fills your screen and is more immersive. Supposedly fullscreen mode provides better performance, but I don't anything about that (nor have I recently observed better performance in fullscreen mode). The most common caveat is that your computer chokes momentarily if you alt-tab to go do something else. Playing in windowed mode allows you to switch to other tasks with no delay, or even multitask. Windowed mode also seems to be better for users using dual displays.
In Maximized Fullscreen mode, the game is in windowed mode, but the borders and title bar are removed and the resolution matches your desktop's. In effect, it looks like you're playing in fullscreen mode, but you can still switch to other applications with no delay. Sounds like the best of both worlds to me!
Multitasking is great if I happen to be respawning, waiting for a loading screen, or if I need to look up information about the game (like looking up quest info for MMOs). Clicking on the game pushes the other (naughty, immersion breaking) windows and the taskbar into the background, seamlessly filling the full screen.
Unfortunately most games don't seem to include this feature yet. For the games that don't, is there a way I can force this mode?