PCSX2 is the only working PS2 emulator being develoeped right now (at least the only one worth mentioning anyway) but unless you have a very powerful computer the games will run extremely slow. As with any console emulated that runs from CDs or DVDs this emulator will allow you to use actual PS2 discs to run so if you have any PS2 games there is no need to download them. Just stick them in your disc drive, set the emulator to read from that drive and play (assuming that game will work in the emulator in the first place that is).

You can find the latest news and downloads for PSCX2 here:
http://www.pcsx2.net