I can’t get by with less than two monitors.
Most of the time, I have mine set up so that my tax/bookkeeping software appears on one screen and the other screen is used for Word (where I keep client-specific instructions and notes on the work I’ve done) or for Acrobat (where we have scanned bank or tax statements). For me, it’s not a matter of multitasking, but of keeping more of the components visible at once.
Development mode
Dual screen is perfect for writing VBA code in excel. One screen has the
spreadsheet view and another has the code view.
Run mode
One screen to run program and monitor
Second screen to browse SDMB 
Dual monitors seemed silly to me when I first encountered it, but once I started using it at work, I find it difficult to imagine working with only one again.
At work, I’ll often have things like e-mail and IM client open on one to keep an eye on them and whatever I’m working on on the other. If I’m making configuration changes or whatever, I’ll often have documentation or settings or other reference material on one monitor and work on the other. It really shines when I’m coding though. I have code up on one screen and I’ll have test runs or results on one screen, or a browser to some reference code, or whatever else I need on the other. Basically, I can work full screen on something and not have to alt-tab, which helps me maintain my focus. Sure, I could work with one screen and have each thing take half the screen or whatever but, especially with code, I really need a full screen to work on it.
At home, it’s just as useful. It’s nice to be able to look at other webpages simultaneously when I’m writing e-mails, posting on facebook, or posting here. For instance, I can have a reference for a post open and be looking directly at it as I’m composing a post. It’s not to uncommon that I’m sort of half-watching a youtube video or whatever while I’m looking at other stuff. It really shines for gamers. Some games can take advantage of multiple screens, like putting the game on one screen and a map and other references on the other so your UI is less cluttered and you get greater detail. I play WoW, so I’ll often have that on one screen and Mumble and material related to what I’m doing (strats, loot, armories, forums, etc.) on the other; as a GM and raid leader, having to alt-tab constantly would be extremely distracting. Hell, it’s nice to be able to keep an eye on other things if there’s down time or I’m just kind of putzing around.
It does take some time to get used to having the extra screen real estate. I know for a while I kept kind of forgetting that I had the second monitor and I’d still keep alt-tabbing or resizing windows. But once I figured it out, I feel like I’m quite a bit more productive and I feel crippled when I am stuck on one monitor.