It was a summer tradition for Many Years that is now gone.
The Justice League / Justice Society that many of us grew up on haven't happend in the New 52.
Yes I do know that Power Girl and Huntress have met Superman and Batman. but that crossover doesn't take them to Earth 2. I yes I do recall that there is are stories where Earth 1 and Earth 2 Supermans and Batmans meet as well.
But some of the best stories I have ever read came out of that annual event.
The possibility of that happening again is still murky. The Earth 2 title is made up of people teaming up, and not a team.
I thought, at first, that the apperance of the Crime Syndicate would usher in more crossovers. That is not the case.
So if you are interested in these stories, please consult the link provided here: http://en.wikipedia.org/wiki/Justice_Society_of_America#Guest_appearances_in_Justice_League_of_America_and_others_.28Silver_Age.29 This Wikipedia page not only gives the history of the JSA, but mentions The Justice League crossover issues.
This link can get you digital copies of the stories for less than over the counter copies.
Now I am going to tell you my 10 Favorite team ups.
10. Justice League of America Vol 1. 100-101 -JSA/JLA and The Seven Soldiers of Victory Villian: The Hand. http://dc.wikia.com/wiki/Justice_League_of_America_Vol_1_100
9. Justice League of America Vol 1. 195-197 JSA/JLA versus the Secret Society of Super-Villians
8. Justice League of America Vol 1 183-185 JLA/JSA/ New Gods versus Darkseid
7. Justice League of America Vol 1 159-160 JLA/JSA, The Heroes of Yesterday: Jonah Hex, Viking Prince, Miss Liberty, Black Pirate, and Enemy Ace Versus The Time Lord.
6. Justice League of America 207-209, and All-Star Squadron 14-15. JLA/JSA and the All-Star Squadron versus Per Degaton.
5. Justice League of America 113. "Creature in the Velvet Cage" JLA /JSA versus Sandy the Golden Boy. http://dc.wikia.com/wiki/Justice_League_of_America_Vol_1_113
4.Justice League of America Vol. 2 #0, 8-12; Justice Society of America Vol. 3 5-6 JLA/JSA and the Legion of Super Heroes. The Lightning Saga http://en.wikipedia.org/wiki/The_Lightning_Saga
3.Justice Society of America Vol. 3 #43; Justice League of America Vol. 2 #54-60
The Rise of Eclipso. JSA /JLA http://en.wikipedia.org/wiki/Eclipso#Rise_of_Eclipso
2. JLA / JSA "Virtue and Vice" graphic novel. JLA/JSA vesus the 7 Deadly Enemies of Man.
1. Justice League of America "Crisis on Earth X" JSA/ JLA and the Freedom Fighter versus modern day Nazis. http://dc.wikia.com/wiki/Justice_League_of_America_Vol_1_107 to buy digitally here are two links
That is my list. You may disagree with it, or you may not. All of these books are available digitally via Comicology.
That is all I have for now.
Go Forth and Do Well