What bands have the most unique sounds you've ever heard. For me: The Mars Volta.

Nothing is more or less unique than anything else. Just grammar in everyday life, kids.

Sigur Rós

fantomas

I would disagree, but I'm not entirely sure I understand your point.

Stick around. We'll fix this. And that really needs to be fixed.

Seriously, it's difficult to think of things in terms of "uniqueness" given the degree to which things are copied/ripped off...The Beatles, Hendrix, Floyd, etc...given their over-saturation, you wouldn't think of them as unique today. Also, the difference between "uniqueness" and "innovation" can be hard to define.

I'll just assume you're looking for "weird" as opposed to "innovative"...and given "bands", I'll stick to Rock...

In which case, here's an off-the-top-of-my head, concise list that should tide you over:

1st:
Zappa/Mothers
Beefheart/Magic Band
Can
Faust
The Residents

2nd:

Magma
Henry Cow/Art Bears
Red Krayola
Fushitsusha
Gong
This Heat

Honorable Mention:
Area
Volcano The Bear
Art Zoyd
Plastic People of the Universe
Alamaailman Vasarat
Uz Jsme Doma
Tiger Lillies
Boredoms
Nurse With Wound
No Neck Blues Band
Pere Ubu
Sleepytime Gorilla Museum
Ruins
Mr. Bungle
Animal Collective
Diablo Swing Orchestra
Gogol Bordello


Not in "rock" and not "bands", but can't be left out of this sort of list:

Harry Partch
Sun Ra
Moondog

Unique is a superlative. If something is unique, it's not *more* unique than something else.

Indeed.

no one has uniquely sucked as much as Vanilla Ice

No much to add after Seba's list, specially first 5. Maybe some that haven't been mentioned are:

The Pop Group
Royal Trux
Robert Wyatt
Foetus
Peter Brotzmann (jazz)