You would like Prince of Persia - Sands of Time is the best in my opinion, the first in the series for ps2. cheap second hand on ebay. It's quite similar to tombraider in many ways, with alot of climbing and jumping and puzzle-solving in fantastic locations. There is also a Prince of Persia on xbox360 now, but I don't think it is as good, although of course it looks a whole lot better (and costs a whole lot more as it hasn't been out too long).
Another very good 3rd person action adventure game is Beyond Good and Evil for ps2 -
http://uk.ps2.ign.com...les/440/440103p1.html - should be very cheap 2nd hand on ebay now.
Other good platforming games similarish to rayman for ps2 are Ratchet and Clank and Psychonauts. Also the various lego games are fun ie starwars, indiana jones etc, although I find them a bit too repetitive.
Being a point and click adventure, Syberia is very slow paced with no action element whatsoever but is well regarded by people who play adventures. i've played through it but i've never really been into adventures so found it waay too slow. It is atmospheric though. You could try it though as it would be really cheap 2nd hand