And covered earlier by the Who, so it figures that the Jam would cover it.
My vote is for Ted Nugent’s cover of George Harrison’s “I Want to Tell You.” The overdriven guitar works wonders with the main riff/head of the song, and Charlie Huhn’s vocals are pretty good as well.
Speaking of good cover versions, this cover of Outkast’s ‘Hey Ya’ is pretty fucking awesome.
For those interested, the singers name is Mat Weddle, and his band is Obadiah Parker
Wilson Pickett’s cover of “Hey Jude” blows the Beatles’ version out of the water, IMHO.
It’s one of only a couple of Beatles covers that I prefer to the original.
Juliana Hatfield regularly does a cover of Weezer’s “Say it ain’t So” in concert, that is light-years superior to the original.
I’ll second CvB’s “Pictures of Matchstick Men”
The Blue Man Group’s cover of the Who’s “Baba O Reilly” is stellar. Plus, I just love Tracy Bonham to pieces 
…was itself a cover version, IMO superior to the original by The Byrds.
It’s Dylan’s song. He not only wrote it, but he recorded it first. How is it a cover?
That does sound really good. I bet iTunes isn’t going to help me find it, either.
That’s a good example of a surprising cover - who would have thought Kurt Cobain liked Leadbelly?
I wasn’t surprising that Thom Yorke from Radiohead sang on a cover of Pink Floyd’s Wish You Were Here, done by Sparklehorse. I WAS surprised that I like it better than the original. Yorke made one of two good changes in the lyrics (like changing “pain” to “rain” in the first verse), the tempo is slower, and it’s way more emotionally charged.
I like the concept of cover versions. (As long as the cover version is sufficiently different from the original.) Already a lot of good covers have been mentioned. Unfortunately I couldn’t find the say it ain’t so cover. I love that song.
Anyway, some more:
Beseech - Gimme gimme gimme
Dread Zeppelin - Your time is gonna come (Their other covers are ok. This one i probably better than the original.)
Also, not really a cover, but the mash version of Vines - Get Free, and Pink - Get the Party Started is surprisingly good
Oddly enough, the Dresden Dolls’ cover of “War Pigs” came up as I clicked on this thread. It’s a live version, so it’s just the piano and drums, and Amanda singing the hell out of it, and it’s fantastic. They get an amazingly heavy sound out of two instruments.
The Gourds do a bluegrass version of “Gin and Juice” that I absolutely love. I’m starting to think that every song needs to be done in a bluegrass version at least once.
Also worthy of mentioning - Ted Leo’s version of “Since U Been Gone” and Travis’ live cover of “Hit Me Baby (One More Time),” with the audience cracking up intermittently.
SMDB syndrome: other posters already mentioned Jeff Buckley’s cover of Hallelujah, as well as Stevie Ray Vaughan’s cover of Little Wing.
Please don’t crucify me if I actually liked Dilana (of RockStar Supernova)‘s version of Psycho Killer almost as much as the original Talking Heads’ – though they’re pretty amazing too. Hers just sounds more contemporary.