You can use pretty much anything to copy games, Nero, Alcohol etc
However unless you have a chipped PS2 you wont be able to play them.
On the PC side of things most new games have copy protection, however most can be cracked by using a site such as www.gamecopyworld.com
If you want to play copies on your PS2 then the best bet is to get a hard disk (internal or USB depending on the model of the PS2) and then get HDAdvance as that lets you copy the game onto the hard disk and then play it from there without needing the original.