Many regard the Pcsx2 emulator as the best Playstation 2 emulator in existence and I have to say that it really does an awesome job as long as your computer is fast enough to handle the emulation. There are two prerequisites that are a big hurdle for many users. The first is that you do need a Playstation 2 bios file.
The developers can't supply one because they would infringe on Sony's copyright. It is possible to use tools to extract the bios of your own Playstation 2 but that requires at least some technical knowledge to get started.. Iknow that most P2P networks have those files available as well. Note that it is not legal to download the bios from these sites though. Besides the Bios you also need a game obviously before you can play Playstation 2 games.
Those games can be in all image formats like iso, img or bin. A plugin also adds compatibility to put Playstation 2 games in the CD or DVD drive and play them from there. I highly recommend playing games from disk images as it is not only a lot faster, due to faster loading speeds, but also better for the original PS2 discs as you do not have to use them while playing the games on your PC.
The compatibility list is incredible. It lists 1858 Playstation 2 games of which 748 play perfectly. New versions of the emulator will surely increase game compatibility further.
I would like to point out two important features of PCSX 2. The first is that you can add plugins to it that enhance the functionality much like the one I mentioned above that is adding the possibility to load CDs and DVDs from the drive directly.
The second is that you should consider playing those games with a Playstation pad because it is really awful to play a game like Tekken with the keyboard.
Update: The Playstation 2 emulator has been updated throughout the years. The version at the time of writing supports more than 2300 PS2 games of which almost 75% play fine. A good starting point is the compatibility list which you should check out first to make sure the games you own play fine in the emulator.
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