It seems like there are hundreds of covers of this song. For me, I gotta go with The Doors’ version. Just something about Jim Morrison singing it that makes it better than anyone else.
Maybe it’s because it was the first version I heard, but The Weavers’ version was my favorite. Next would be The Animals, even though they took some serious liberties with the music.
My favorite, by a longshot, is Snakefarm’s. Anna Domino is a god.
Blind Boys of Alabama doing Amazing Grace to the tune of House of the Rising Sun. So groovy, and cool.
Andy Griffith
No kidding.
It’s on Golden Throats, Vol. I The lyrics are so changed that the song is about — well, it’s about nothing, as far as I can tell. Certainly not about anything as sordid as a bordello. A surreal experience.
Roscoe Holcomb’s.
Mike Auldridge’s dobro instrumental.
I was gonna pop in here and say Holcomb’s, sure that no one would have beaten me to a relatively obscure version like that. But hell yes. Good Lord, his version is spine-tingling.
Failing that, Nina Simone’s house-rockin’ version.
I’m going to be unimaginative and go with the Animals.
The best version is by the Twisted Christmas people. They sing it with the words of Oh Little Town of Bethleham. It’s awesome.
No, no, no you Philistines.
The best, never to be bettered, rendition of House of the Rising Sun was by Joan Baez in one of her Vanguard albums in the early sixties. It only beats the Weavers by a little bit. The first time I heard that pure soprano of her’s my breath caught in my throat. It was like chugging a shot of cold gin–that pure and sharp. Oh, Lord, to be eighteen again and to hear that lovely voice for the first time.
Tori Amos
Sinead O’Connor
Her version is a little more creepy than melancholy.
Frijid Pink.
Much as I love the Animals, this amped-up, fuzzed-out version puts shivers down my spine. Elicits more anguish than self-pity, IMHO.
Yes! Also, I always felt male singers doing this one was just a bit odd…
My highschool band, Fat Man’s Fridge, we rocked!!!
Bob Dylan
I too have to give points to Ms. Simone for her surprisingly upbeat treatment of the song.
I vote for Dylan also. If you didn’t know what the song was about, you’d not get a clue from the Animals’ version.
Best parody: 5.01 - named for an infamous freshman chemistry class that I never had to take 
*There is a course, at MIT
They call it 5.01 (pronounced five oh one)
It’s been the ruin of many a poor tool
Lord, I know I’m one
**
I’m currently enjoying ** The Be Good Tanyas ** version. I do love them.