Yeah, I've heard that one.  I like it as well; I just failed to remember it when trying to remember all the covers I loved.

The Lupe Fiasco one requires you to like rap, so I can understand that not being everyone's cup of tea.

Here are a few more "covers" by basically a child prodigy at the acoustic guitar.  Some of his earlier videos are just mind blowing.  A self taught 8 year old should not have been able to do what he did.

This one is probably blasphemy in one form or another to most people, but I think his rendition edges out Michael's original for me.  I think it has more to do with me not liking old sound quality than anything else:

This second one, I don't think I can say it's better than the original, but it's still a really great cover:

The Clash - I Fought The Law

Aerosmith - Come Together

Reel Big Fish - Take On Me

Of the stuff mentioned in this thread:

• Rufus Wainwright's Hallelujah is genius
• As far as I'm concerned Alice Cooper has the only version of Poison (well, him and Bel Biv and Devoe but that's a different song)
• The Goldfinger version of 99 Red Baloons is great
• I love Fiona Apple's version of Across the Universe, it's the best thing about Pleasantville (and I even like that movie)
• stopped reading the thread about the above video >_>

As for some covers I like better than the originals (and I in general actually like covers better):

• I Want to Hold Your Hand - Across The Universe Soundtrack
• Touch-a Touch-a Touch Me - The Chubbies
• I Want You to Want Me - Letters to Cleo
• How Deep is Your Love - The Bird and the Bee
• The Boys of Summer - The Ataris
• Nothing Else Matters - Bif Naked
• I Will Survive - Cake
• The Man Who Sold the World - Nirvana
• Mack the Knife - Ella Fitzgerald
• Spoonful - Etta James (I don't think she was the first one to record that was she?)
• Killing Me Softly - Frank Sinatra
• Most anything by the Glee cast

There are many more, but can't spend all day looking through my music for covers I love.  ;_;