The original, "The Thing From Another World," is a truly terrible B-movie classic worthy of MST3K! Totally worth watching to see the masterpiece they turned the story into. The Mary Elizabeth Winstead one, same name, different movie, wasn't too bad either.
Horror Express with Peter Cushing and Christopher Lee, which I've never seen. William F Nolin, who did Logan's Run, wrote a version, but it was never filmed. Couldn't really find any others, but I'm sure there are.
I also just found out tonight that there's a fan film called The Thing Returns that looks so terrible I have to see it.
Also, there's The Thing video game for PS2, Xbox, and Windows. Carpenter apparently considers it to be a canon sequel and the events in it clarify what happens at the end of the first movie.