From 1963-1985 DC produced an annual visit of comics original Super Hero Team - 
The
...
 
in their Silver Age team flagship, 
The

 
From their initial encounter "Crisis on Earth One" (JLA 21) & "Crisis on Earth Two" (JLA 22) the two teams were involved in all types of universal...well...Crises! (Crisis on Earths 1, 2, 3, X, S Prime, the 30th Century, the past & future, Between Earths 1 & 2, Apokolips, and Limbo -to name a few!!)

Over the years the two groups were joined in their adventures by groups ranging from The Seven Soldiers of Victory and The Freedom Fighters, the 30th Century's Legion of Super Heroes, The Marvel Family and Golden Age Fawcett Heroes, and The All Star Squadron and Infinity Inc.!  Unfortunately the annual tradition came to an end with the Crisis on Infinite Earths in 1985.

However in 1993 the JSA assisted the Justice League Europe in a three part adventure against Sonar and as of 1999 the launch of JSA promises an annual team-up yet again.  Indeed this has even started with a team up in JLA 28-31 "Crisis Times Five" as the League and Society battle against a threat from the Fifth Dimension.
It all started in "The Flash"
Flash No.123 "Flash of Two Worlds"
Flash No.129 "Double Danger on Earth"
Flash No. 137 "Vengeance of the Immortal Villain"
1963
Justice League of America No.21
"Crisis on Earth-One."
Justice League of America No.22 
"Crisis on Earth-Two."
1964
Justice League of America No.29 
"Crisis on Earth-Three"
Justice League of America No.30
"The Most Dangerous Earth of All"
1965
Justice League of America No.37
"The Earth without a Justice League."
Justice League of America No.38 
"Crisis on Earth-A."
1966
Justice League of America No.46
"Crisis between Earth-One and Earth-Two."
Justice League of America No.47
"The Bridge Between Earths."
1967
Justice League of America No.55 
"The Super-Crisis that struck Earth-Two."
Justice League of America No.56
"The Negative Crisis that struck Earths One-Two."
1968
Justice League of America No.64 
"The Stormy Return of Red Tornado."
Justice League of America No. 65
"T.O.Morrow kills the Justice League-Today."
1969
Justice League of America No.73 
"Star Light, Star Bright - Death Star I see Tonight."
Justice League of America No.74 
"Where Death Fears to Tread."
1970
Justice League of America No.82
"Peril of the Paired Planets."
Justice League of America No.83 
"Where Valor Fails, Shall Magic Triumph?"
1971
Justice League of America No.91 
"Earth - The Monster Maker."
Justice League of America No.92
"Solomon Grundy - The One and Only."
1972
Justice League of America No.100 
"The Unknown Soldier of Victory."
Justice League of America No.101
"The Hand That Shock the World."
Justice League of America No.102
"And One of Us Must Die."
1973
Justice League of America No.107
"Crisis on Earth-X."
Justice League of America No.108
"Thirteen Against the Earth."
1974
Justice League of America No.113 
"Creature in the Velvet Cage."
1975
Justice League of America No.123 
"Where on Earth Am I?"
Justice League of America No.124
"The Avenging Ghosts of The Justice Society."
1976
Justice League of America No.135
"Crisis in Eternity."
Justice League of America No.136
"Crisis on Earth-S."
Justice League of America No.137
"Crisis in Tomorrow."
1977
Justice League of America No.147 
"Crisis in the 30th Century."
Justice League of America No.148
"Crisis in Triplicate."
1978
Justice League of America No.159 
"Crisis from Yesterday."
Justice League of America No.160 
"Crisis from Tomorrow."
1979
Justice League of America No.171
"The Murderer among us : Crisis above Earth-One."
Justice League of America No.172 
"I Accuse..."
1980
Justice League of America No.183 
"Crisis on New Genesis, 
or Where have all the New Gods Gone?"
Justice League of America No.184
"Crisis between Two Earths, or Apokolips Now."
Justice League of America No.185 
"Crisis on Apokolips, or Darkseid Rising."
1981
Justice League of America No.195
"Targets on Two Worlds."
Justice League of America No.196
"Countdown to Crisis."
Justice League of America No.197
"Crisis in Limbo."
1982  "Crisis on Earth Prime "
Justice League of America No.207 "Crisis Times three."
All Star Squadron No.14 "The Mystery Men of October."
Justice League of America No.208 
"The Bomb Blast Heard 'round the World"
All Star Squadron No.15 "Master of Worlds and Times."
Justice League of America No.209
"Let Old Acquaintances Be Forgot..."
1983
Justice League of America No.219 
"Crisis in the Thunderbolt Dimension."
Justice League of America No.220 
"The Doppelganger Gambit"
1984
Justice League of America No.231 
"Family Crisis"
Justice League of America No.232 
"BattleGrounds"
1985
Infinity Inc. No.19 
"Last Crisis on Earth-Two."
Justice League of America No.244
"The Final Crisis."
1993
Justice League Europe No.48 
"Red Winter : The Freeze."
Justice League Europe No.49
"Red Winter : Hard Ground."
Justice League Europe No.50
"Red Winter : The Ice Breaks."
1999
JLA  "Crisis times Five"
2000
DC2000 Book 1
DC 2000 Book 2
2001
JLA Incarnations Issue 1
2002
JLA/JSA Vice and Virtue