I have 2 monitors, but i have a Digital Tuner card, so i simply full screen the TV on the second monitor and then play games etc with my main TFT.
You'll never be able to play a game and still use an app on the second monitor as the mouse is "fixed" to your game screen, so ofcourse you have to alt tab out.

I'm sure there's a piece of software out there somewhere which creates "2" desktops. I know ATI's Hydrovision does, but i found that pretty slow and it didn't really achieve what i wanted it to.

At the end of the day, the pros i see for having 2 monitors are
- being able to move MSN/Xfire etc chat windows to your second monitor while playing a game, so that you can see if someone talks to you
- moving task manager over there so if a game crashes on a black screen, you can move over to the second monitor and end the process simply.
- TV as i've said
- Putting up a FAQ or any other text which you want to copy or read. If you have to type a straight copy of something over, you can have both up at the same time.
- You look cool on the Steam survey ;p

You can always find a use for it, hopefully some of those points will make you feel better about having 2 screens.
I've yet to experience problems with any games on a dual screen setup, and even Pro Evo 5 works when it's not the active window. Therefore you can click and type on apps on your second monitor, and still play it with the gamepad. It's the only game i've found to be like that tho. Most others freeze while they're not active.