Well, i had jdk1.6.0_01 64 bits and eclipse 3.3 on ubuntu and worked fine, but i was having problems starting tomcat, so i switched back to 1.6.0 and tomcat started working, but eclipse stopped with the same error... I have another box, running a suse based distro with jdk1.6.0 64 bits but the eclipse version is 3.2, and it's working perfectly. I don't have a clue of wath's going wrong, but I'm going to try to switch back to eclipse 3.2 on the ubuntu box...
I know this is not helping anything, but I'm just sharing a similar problem.
Cheers,
Hernāni