Mine’s got to be Rocket Man, covered by William Shatner!
Though Peter Sellers covering She Loves You in character as Dr. Strangelove is a strong second.
Hendrix’ Star Spangled Banner!
Or the Stewie version- the best part of that is his little dance at the end.
The Bobs, an a cappella quartet, used to do a cover of White Room that kicked ass.
Actually, they still do it (found a video), but they’ve changed a couple members since then, and on this song it’s just not the same. Janie Bob used to sing lead and could bring down the house. Richard Bob’s bass still sounds fantastic, though.
Nouvelle Vague’s version of Too drunk to fck *(Dead Kennedy’s).
In college, I knew a guy who sang “Jukebox Hero” in grand opera style.
Van Halen’s cover of “Happy Trails” was sort of amusing.
I am told that Wayne Newton covered “Enter Sandman”. I’m curious to hear that.
Gotta be Paul Anka’s cover of Smells Like Teen Spirit.
Wow.
Just wow.
I really like the Foo Fighters’ version of Prince’s Darling Nikki. Recently heard the Violent Femmes doing Gnarls Barkley’s Crazy- that’s fun.
I’ve got to go with this one.
Though if Yes’s cover of America (written by Simon & Garfunkel) counts that would be my top pick. The song is very different in the Yes version and much, much better.
I love The Scissor Sisters’ version of Franz Ferdinand’s “Take Me Out” (apologies for the quality of this video) that I think is in no small part a throwback to Elton John’s “Bennie and the Jets”.
I love YouTube, here it is livein all of its 11 minutes of Glory!
On the same album he also covered Wonderwall and Black Hole Sun.
Genius. Pure genius. 
I can’t say for sure it’s my favorite, but I think Devo’s cover of (I Can’t Get No) Satisfaction definitely gave the song a twist.
Is it really sad that the first song I though of was David Hasselhoff’s Hooked on a Feeling?
It is just awesomely weird…
Ministry’s Lay Lady Lay
I listened to a bit of that, about 25 seconds. It might be the worst thing ever. That was truly awful and I am not a Soundgarden fan.
Coil covering Tainted Love
Outkast - Hey Ya!
Mat Weddle of Obadiah Parker on a guitar doing a cover of Hey Ya.
I love them both!