The DC Universe was once a canon world with just a few twists. Instead of one set canon-point, its history lets off at different time periods depending on the teams/characters, such as Gotham City recently surviving the War Games with the threat of Black Mask still looming over the city, and the Green Lantern Corps being restored to its former glory. There are twists such as Stephanie Brown not dying, and Shiera replacing Kendra as Hawkgirl.
With the arrival of the Crisis, so many things changed. Still, the past remained the same this time. Yet, this is a blessing and a curse, as those of the DC Universe find themselves learning a secondary history and finding their daily lives often turned upside down, and a bit harsher world than they are perhaps used to.
Justice League cutoff is pre-Infinite Crisis. The headquarters is in the Watchtower, 22,300 miles over the earth.
Max Lord is dead, having had his neck broken by Wonder Woman on live television to the whole world after he had taken over Superman's mind. Wonder Woman has since been forgiven for what she did by the world at large.
JLI & Super Buddies
The Justice League International had their plot 'Can't Believe it's not Justice League', published as JLA: Classified did happen. Though Captain Marvel declined membership, his sister Mary Marvel did join and was a roommate to Fire.
Supergirl a.k.a. Kara Zor-El crashed in the Gotham Bay. She was trained by the Amazons, and later kidnapped by Darkseid. She was rescued by Big Barda, Batman, Wonder Woman, and Superman. Her death was not faked during the rescue, instead Supergirl banded with Superman and fought Darkseid together before stranding him in deep space via a boom tube. Supergirl never joined the Outsiders as the Nightwing and Arsenal version was never founded. The Kryponite Poisoning and Krypontian Ghosts story arc never happened. Kandor never happened.
Linda Danvers is still nowhere to be found, having retired from being the former Supergirl. She has not become the Angel of Fire, and the Reign in hell story arc has not happened.
Superman was there when Manchester Black committed suicide, and he and Lois Lane are still happily married. Superman has not gone wondering the country on foot, but did begin to have concerns over his title, leaving it to Superboy to carry while he searches for himself in mentoring the next generation of heroes.
Hal Jordan has only just returned to life, and the other corps have not formed at this time. Kyle is not Ion, the entity ended up going somewhere else, and Alan Scott is not working with Checkmate, though he does work solo as a hero since the Justice Society of America has gone inactive. Furthermore, Jade is alive and well, and also working solo.
When Hal Jordan became the Parallax there were those that will forever hold a grudge. And when all thought he breathed no more, a confrontation with Psycho Pirate had his spirit separated from the Spectre and once more returned to his human body. Living and breathing once again, he is assigned to Sector 2814 with John Stewart.
Kyle Rayner did not have it much better, though he managed to avoid becoming Ion (the entity possessed someone else). He is still one of the few Green Lanterns that has less trouble with the Yellow Impurity, and though he is often on Earth and a member of the Justice League, he is technically stationed on Oa as a member of the Honor Guard.
The Guardians also did decide to reinstate the kill restrictions on the power rings after the Sinestro War and its clean-up was completed.
Jesse Quick is actively running her company, and still holds her speed powers and of course her delightful mother issues, and rocking it out single (for now).
Damage is still delightful whole, but never did join the team.
Hawkman is still the Pharaoh, and before Kendra could join the Justice League, she was murdered by Hath-Set. Upon Hawkman's return from the Rann Thanagar War, he discovered his beloved dead once more. He searched for any that would help him, but only Dr. Occult stepped forward. During the resurrection ritual, Shiera Hall became alive. It was only some time later, that it was discovered Kendra was also resurrected with a fresh start.
The following story arcs have happened for the Aqua-Family: The Imperiex War, Obsidian Age, War with Cerdia, and Sub Diego. Black Manta is also dead, though Mera - King Arthur's wife - is alive.
Aquaman is spending a good deal of time on the surface world, but still rules Atlantis with those he trusts.
Athena has taken over Olympus.
Wonder Woman is no longer blind, and has killed Max Lord.
Donna Troy is still deceased, having been killed by a Superman Robot during Graduation Day.
Artemis is still on Themyscira. Therefore, Themyscira is still there and has not been destroyed by Imperiex. Nor has the Amazon uprising against Man's World happened.
Green Arrow returns from the dead, encouraging his son to continue going by the same codename as well. He goes on a road trip with Roy Harper to fix their broken relationship. During Archer's Quest, it is discovered that Ollie knew he had a son and regrets not being there for him, and his attempt to ask Black Canary to marry him fails.
During City Walls story arc, Star City is enclosed in a magical bubble that no one can get into. Demons kill those that commit crimes. Mia earns her write to become a member of the Arrow Family during this time, and with all of their hard work, the mix-matched family manages to get the cops and criminals to behave to stop the demonic slaughters. When they all work together to storm Albert Davis' house, they discover the only way to stop the spell is to kill him. Speedy makes the fatal shot when Green Arrow can't, the decision haunting her.
Arsenal is currently with the Titans, having not refound the Outsiders with Nightwing. He lives in Titans Tower with his daughter Lian with Rose Wilson as her nanny. He is still a whole man, and a loving father.
Batman's Outsiders has happened, but has since broken up.
Former members of the team are currently working solo or doing their own thing, but the team could be reformed. Indigo is still non-operational and under the control of S.T.A.R. Labs.
Jason Todd is (currently) dead, and Damian Wayne does not exist.
Nightwing is haunted with his own mistakes. Blockbuster is in a coma with little to no chance of ever recovering, after both Parkthorne and Halye's were destroyed. Though the evens of Nightwing #91 did not happen, and Tarantula's advances were fended off. She has since died.
Catwoman helped the Bat Family out during War Games. She has also built up her own Cat Family, as she works as a semi-vigilante in the East End. Just after War Games, Holly Robinson threw a surprise birthday party for Catwoman, and it reminded her of just how much she is loved and supported, even by Batman.
Titans & Young Justice
A Kid's Game story arc had happened, and Graduation Day did occur for the most part. However, though Donna Troy still died, the Titans as a team worked together to defeat the Superman Robot rather than Indigo with her one punch. Indigo is under repairs and control of S.T.A.R. Labs right now.
Jericho was separated from his father Deathstroke, and is currently stored on the Titans database system, until they can figure out how to bring him back. As a precaution, he is also regularly copied on a backup system in storage, though Beast Boy regularly visits him in the main database so he doesn't get lonely.
Rose Wilson's foster parents are still alive, and she lives with them in San Francisco. She currently babysits Lian Harper a lot, and will occasionally help out the Titans in times of need. Her relationship with her father Deathstroke is questionable, though they have had contact since he last dropped her off at the Titans Tower.
The Titans is currently a large team with the Outsiders never refounded by Nightwing and Arsenal. They are split in Junior and Senior teams, and have seen much growth since the Young Justice disbanded and joined the Titans.
Many of the newer Titans such as Miss Martian, Zatara, and Jaime Reyes, have not yet been introduced.