I am 21-years-old, and I lived with my parents until mid-September of 2006. From 2002 through November of 2006, I was a full-time student, working full-time in summers and from May 2006 through the end of the year. On my 1040, can I claim 1 exemption for myself, or am I considered a dependent of my parents?

Yes, they can still claim you as a dependent. If you make less then $10K a year you don't even have to file taxes. You will get dingged if you file and they file you as a dependent.
See a tax preparer though. I am sure there are ways around it.

AtYourService:

Where did you come up with the less than $10K figure?? If Smashley lets his parents claim him, the standard deduction is only $5,150, which means taxes would be owed on as little at $5,500.

You are right that his parents can still claim him (though this is the last year for that).