Well my dh and I are right now in the middle of the wonderful project of remove self-stick tiles that my daughter had stuck on the hardwood floors of her bedroom. Two hours into the project, testing out the suggestions here, I can tell you what we have learned.
(1) a hair dryer helps greatly in removing the tiles in one piece.
(2) apply paint thinner/solvent with a spray bottle, then scrape with a putty knife, and wipe residue off with a rag. You may have to do this a couple of times to get it all.
(3) this is not a quick project, but will be well worth it once we get the floors sanded down and polyurethaned.
(4) never, never, NEVER use self stick tiles on a floor you care about!