Well, the original launch consoles have the ability of full backwards compatibility. They are the 20GB and 60GB versions. However, they've been out of production for a while, so don't expect to find one new for as much as a used one. Most of them are starting to experience problems about this time in, so while they are a nice investment, you should know that because they're older, there's a chance you'll have to pay $150 to get it fixed by Sony on top of what you have to pay to buy.
The older 80GB models (Phased out with the Metal Gear Solid Bundle) only have one chip from the PS2 that allows them to play games through emulation. As opposed to the 20GB and 60GB models, these bad boys only offer about 80% playback with PS2 games. A more updated chip set, and I think a better fanning system, these guys are slightly more reliable than the 20GB and 60GB models, but as aforementioned, they're being phased out, if they haven't been already.
The 40GB and New 80GB models (as of August 2008) are not backwards compatible.