Bizarro Justice League

Silver Age
Bizarro stole Lex Luthor's imperfect Duplicator Ray that created Bizarro clones. Bizarro created a cube-shaped version of Earth with natives that were warped clones of the natives of Earth. Among these were the Bizarro Justice League. This version of the team had the powers of their "normal" counterparts, but had backward logic. Despite popular belief, the team does say what they mean (not the opposite), but with bad gammar. Members were:

• Bizarro Aquaman
• Bizarro Batman- World's worst detective and died to save Batman
• Bizarro Flash- His costume had the reverse colors of Flash (similar to the Reverse Flash), but had a gravel logo (because the Flash was holding one at the time of cloning).
• Bizzaro Green Lantern (a.k.a. Yellow Lantern)- He was given a yellow power ring by mistake and couldn't use his Green Lantern battery to refuel it (this verison of the ring couldn't affect anything green), leaving him powerless. He was the most scared being in the entire universe (as oppose to the fearless Green Lantern).
• Bizzaro Hawkman
• Bizzaro No. 1- Impefect clone of Superman and the leader
• Bizzaro Wonder Woman

Crisis on Infinite Earths
The Bizarro World (and everyone living there) was destroyed.
Modern
As a result of the Emperor Joker story arch, a new Bizarro, Bizarro III (Bizarro II had no connections to the League hence not being mentioned), was created. Under a blue sun, he got a power called “Bizarro Vision”, which had a similar effect as the Duplicator Ray mentioned above. He recreated the Bizarro World, but plotted to destroy it and kill everyone, but himself (as Superman would never do that). So, Bizarro Lex Luthor led a revolt and freed the Bizarro-Doomsday to stop him. So, Bizarro recreated the Bizarro JLA to stop it. They defeated the monster, only to let Bizarro destroy the Bizarro World! Member were:

• Bizarro Aquaman- Can't swim
• Bizarro Batman- World's Worst detective
• Bizarro Flash- Fat
• Bizarro Green Arrow- Sets his arrow backward
• Bizarro Green Lantern- A Sinestro Corp member. His ring actually works.
• Bizzaro Hawkgirl- She has the intelligence of a hawk.
• Bizzaro Wonder Woman- Thinks men are superior

Other Versions
In the DC Super Friends # 18, team called the Bizarro Super Friends (loosely based on the Bizarro League) appeared.
References:
DC Encyclopedia

http://dc.wikia.com/wiki/Bizarro_Justice_League_(Earth-One)
http://www.comicvine.com/bizarro-jla/65-47966/
http://dc.wikia.com/wiki/Bizarro_Justice_League_(Earth-One)http://www.comicvine.com/bizarro-jla/65-47966/http://dc.wikia.com/wiki/Duplicator_Ray
http://dc.wikia.com/wiki/Bizarro_Doomsday_(New_Earth)
http://media.comicvine.com/uploads/0/40/216488-64487-bizarro-jla_large.jpg
http://dc.wikia.com/wiki/Bizarro_Hawkgirl
http://www.comicvine.com/bizarro-aquaman/29-47973/
http://www.comicvine.com/bizarro-green-arrow/29-47974/
http://www.comicvine.com/bizarra/29-62046/
http://www.comicvine.com/dc-super-friends-this-am-not-the-title/37-167962/
http://www.aquamanshrine.com/2009/08/dc-super-friends-18-oct-2009.html
http://www.hyperborea.org/flash/bizarroflash.html
http://en.wikipedia.org/wiki/Batzarro
http://dc.wikia.com/wiki/Bizarro_Justice_League_(New_Earth)
http://www.comicvine.com/yellow-lantern/29-47971/