You can, but I’m not sure how. There are sites detailing the process however.
On the PCSX2 homepage you can see that it can run lots of PS2 games at a couple frames per second (sometimes it is less than 1 frame per second). But for about 10 or 20% of the cost of one of those fast PC’s you can get a real PS2 which plays the games at excellent framerates…
The PCSX2 FAQ:
http://www.ngemu.com/forums/faq.php?faq=pcsx2_faq
That’s Playstation 1, the query was for Playstation 2. I bought Bleem a while ago, which did a half decent job at some games. In the end the emulators can get really good, the top of the bill emulator I know is STeem, which emulates the Atari ST home computer and it works with all games, demos, all peripherals, etc., in a way that is superior to the original machine.
Bios copyright IS an issue, and outside of STeem (Atari being bancrupt and the BIOS generally being accepted as in the public domain), most emulators are somewhat illegal. There’s a grey area when you own the original yourself, but even then there are rights to be dealt with. Both Bleem and the hardware card for getting a PS1 into your PC were succesfully challenged by Sony in court.