As geforce said, most recent video cards ship with a VGA connector and a DVI connector... in order to use dual monitors, you need a DVI to VGA adaptor (unless you have a fancy LCD monitor )..
the other option is to throw in another video card. If you already have an AGP card, you can probably pick up a crappy PCI card for cheap... but it's probably not really worth it, unless you need to have a huge desktop (like 2048x768 or something)
to do a relatively cheap dual monitor setup, the ATI Radion 7500 is a good solution
It has everything you need in the box and has very easy to use setup utilities.
With a dual monitor setup, you can have each monitor running at a different resolution, refresh rate and color depth.
If you tend to have multiple programs open and flip between them alot, then a multi monitor setup would be a benefit.
The computer will most likely "remember" which application runs in which window... for example, I have a small 17" screen which I use as a second monitor... and when I lauch email, it always opens full screen on the smaller monitor.. which photoshop always opens on the bigger screen.
You can also span a single application over both monitors, however, unless both screens are the same size have a very small bezel (the plastic that surrounds the screen, you will not find the application very usable.