Yes - you can backup ps2 cd format games using your cd burner.
http://www.psxcopyworld.co.uk/Tutorials.htm is a good place to start as they have some excellent tutorials.
You will need a dvd burner if you want to backup ps2 dvd format games to dvd.
You can "rip" psd dvd format games and burn them to cd-r - although this strips out movies/sound of the game and can be a lot of work.
The dvd media itself is not that expensive, you can pick up dvd-r for as little as £2
Hope this helps