Justice Alliance from Earth-D

Martian Manhunter (J'onn J'onzz), Atom, Green Lantern (José Hernandez), Hawkgirl, Hawkman, Wonder Woman;

Green Arrow, Flash (Tanaka Rei), Supergirl (Kara), Superman (Kal-El), Aquaman, Robin, Batman; 

The group appeared in  Legends Of The DC Universe: Crisis on Infinite Earths (1999). 

Published years after the original Crisis on Infinite Earths, this story shows Superman, Flash and other heroes battling the end of their worlds as they reach Earth-D,  where the Justice Alliance makes its first appearance in DC history.

Justice League Europe 1989

The team accordingly to the cover of Justice League Europe #1 of 1989.

Top row: Captain Atom, Flash (Wally West), Elongated Man, Metamorpho
Bottom row: Wonder Woman, Animal Man, Power Girl, Rocket Red 4

Some notes:

Wonder Woman only appeared as a member in issue #1. She never re-joined the team later on.

Wally West had in the beginning the same costume design as the outfit of Barry Allen.

Justice League International 1988

The team accordingly to the Justice League International #19 of 1988.

top row: Martian Manhunter, Guy Gardner, Blue Beetle, Booster Gold, Captain Atom, Batman
bottom row: Rocket Red 4, Mister Miracle, Fire, Ice, Hawkwoman, Hawkman

Fire and Ice joined as Green Flame and Icemaiden in Justice League International #14 (1988)
Black Canary left in #19. 
Hawkwoman and Hawkman joined in this issue. They were reconned as being Fel Andar and Sharon Parker. 

Justice League International 1987

  The characters from the cover of JUSTICE LEAGUE INTERNATIONAL #7, when the series name changed from "Justice League" to "Justice League International".

top row: Martian Manhunter, Black Canary, Mister Miracle, Batman
bottom row: Guy Gardner, Booster Gold, Blue Beetle, Captain Atom, Rocket Red

Justice League 1987

 The characters from the cover of JUSTICE LEAGUE #1.

Martian Manhunter, Doctor Fate, Batman, Mister Miracle;

Doctor Light, Oberon, Captain Marvel, Black Canary, Green Lantern Guy Gardner, Blue Beetle

Justice League (New 52)

The core Justice League team of the New 52 era according to Jim Lee's famous promotional artwork of 2011.

Aquaman, Green Lantern, Wonder Woman, Superman, Batman, Flash, Cyborg

Kingdom Come

Hawkman, Power Woman, Flash IV, Batman, Wonder Woman, Superman

The Ray II, Flash, Wonder Woman in armour, Green Lantern, Captain Atom, Starman VIII

Justice League of America (The Detroit Era)

row 1: Martian Manhunter, Zatanna, Elongated Man, Aquaman

row 2: Vixen, Vibe, Gypsy, Steel

row 1: Batman, Elongated Man, Zatanna, Martian Manhunter

row 2: Vixen, Vibe, Gypsy, Steel

White Lanterns

Several White Lanterns from the events Blackest Night and Brightest Day.

White Lantern Aquaman, White Lantern Batman, White Lantern Flash, White Lantern Hawkman, White Lantern Wonder Woman, White Lantern Hal Jordan, White Lantern Superman 

Justice League of America - Extended Version

As so many people asked for an early 1980s JLA with Martian Manhunter (though he hasn't been present at that time) and Phantom Stranger (though his membership never was really clear): 
HERE THEY ARE! :-)
Dedicated to one of my favourite artists of that time: Dick Dillin!
(His and Joe Staton's work are still inspiring and driving me the most)

Justice League Of America

The Justice League of the satellite era from 1980.
(After Firestorm joined and before Zatannas costume change. Martian Manhunter has not been present at that time as a member. It can be discussed, whether Phantom Stranger should be added or not ;-))

1st  row: Hawkgirl, Flash, Green Lantern, Batman, Superman, Wonder Woman, Aquaman, Black Canary
2nd row: Elongated Man, Zatanna, Firestorm, Hawkman, Atom, Green Arrow, Red Tornado

The Justice League members from the cover of Brave And The Bold #28 in 1960.
(Green Lantern, Flash, Wonder Woman, Aquaman, Martian Manhunter)

The Turnabout League

Wonder Warrior, Superwoman and Superboy from Superman #349

Flash, Black Condor, Superwoman, Batwoman, Wonder Warrior, Superboy from Superman #349