There's a few I can't really comment on since I don't know the original or never even played the games... but it seems like a good list.
I can't for the life of me think of a good remix right now... the only thing that pops to mind is the Final Fantasy prelude theme which has been done so many times. I still think the best one has to be in Final Fantasy VI... it just stays so classic without all the extras they added in other renditions.
EDIT: Wait... being on the Final Fantasy topic, not exactly known for remixes since a lot of songs are originals, but my mind was blown when I realized there actually was a remix of an old song in IX, all the way back from II (NES).
Of course back then I didn't really have access to game soundtracks easily and never played Final Fantasy II so I could never make the connection until much later when someone pointed it out. It's amazing how it's the same song yet sounds so entirely different and awesome.
That's a good one. I guess I never payed attention to it because I haven't played Kirby 64. I usually don't care about remixes I hear in games (sometimes I dont even know they are remixes) unless I've played the original game.