Alternate timelines are created through the artificial alterations to the normal flow of history. There have been several known alternate timelines created, though most of them have been destroyed.
The Savage Time
An alternate timeline created by Vandal Savage giving advanced historical and technological information to his past self during World War II. With the 21st century technology, Vandal Savage was able to take control of Nazi Germany and put the rest of the world on the losing side. In modern times, the Justice League was protected from the changes to the timeline by John Stewart's power ring and saw the result of Savage's interference with history; a totalitarian world ruled by Savage. In this timeline, Batman was a resistance leader that wore thick black armor. Dick Grayson, Barbara Gordon, and Tim Drake were also resistance members.
Death of Superman
An alternate time line where Vandal Savage created a weapon that destroyed all human life but him. This bleak world would go on to reestablish cockroaches as the dominant life, with other animals generally becoming more hostile. However this time line was eliminated when Superman was sent to the future by Toyman's Kryptonite weapon. Vandal was able to send Superman back to modern times, enabling Superman and the Justice League to stop the modern Vandal Savage from completing his weapon.
Static and Gear went back in time 5 years ago where Static/Vigil met his mother to try and save her from apparent death. Though they were unsuccessful, Static's memory of her was reinforced, while his grief over her death was assuaged slightly.
Chronos/David Clinton's Timeline Interference
David Clinton tried to run away from Batman, Wonder Woman, and John Stewart to the Wild West. Clinton arrived and was robbed by Tobias Manning, who used Clinton's future tech to take over the town of Elkhorn while Manning put Clinton in his prison. 6 months later, Batman, Diana, and Stewart caught up and teamed up a Wild West Justice League: Bat Lash, El Diablo, Jonah Hex, and Ohiyesa Smith to defeat Manning.
In the Wild West aftermath confusion, Clinton ran away again from Batman, Wonder Woman, and John Stewart, this time to Clinton's time: the Batman Beyond era. Clinton, now going as "Lord Chronos", collected important historical items, made the Joker's Jokerz his bodyguards, and destroyed most of the Justice League Unlimited, their Metro Tower, and even the Batcave. The surviving JLU members (Terry McGinnis, the Aging Gracefully Static, Warhawk/Rex Stewart, and the Elder Bruce Wayne) used the abandoned Hamilton Hill High School as their headquarters. Sometime later, the JLU saved the present Batman, Diana, and John. During the final confrontation between the Justice League and the JLU against Chronos's Jokerz, both Static and Terry were apparently killed. In the end, Batman and John erased all of Clinton/Chronos's time travels, restoring time to normal.