Yes you can, you can run one monitor from the normal monitor port and another from a USB port but you need a special connector which makes the Air think it has a 2nd monitor attached. Here's an example on YouTube
You need something like the Matrox Dual Head 2 Go which allows you to have multiple monitors with your MacBook. The performance of USB-attached monitors tends to be worse than those connected with display cables so they would be fine for regular computer use but probably not for gaming for example.
With the release of Thunderbolt-capable Macs, you can now drive dual external Thunderbolt displays from MacBooks which have a separate graphics card.