I was watching Star Trek the other day, and although the events seen in that film do alter the Star Trek universe somewhat, I was trying to think of what assumptions can be made. My main assumption is that most of Star Trek as we have seen it still happens. But then what changes will there be? The following is only speculation:
* Whenever we have seen Spock's mother in Star Trek, that will now not happen. So she will not appear in "Journey to Babel" or Star Trek III.
* We can also assume that whenever Vulcan is discussed in any of the incarnations of Star Trek, it is the new Vulcan colony that (old) Spock refers to at the end of the film, it could possibly be named "New Vulcan".
*We see Kirk's brother in "Operation Anihilate", that could now be his half-brother to the person his mother married after the death of George Kirk at the start of the new movie. The person that young Kirk receives a call from when he steals the car at the start of the new movie.
*There is obviously now a different reason that Chris Pike ends up in a wheel chair, but "The Menagerie" can still happen as shown, other than the fact that we must now assume that Pike and Spock visited Talos ("The Cage") on a previous mission before the Enterprise was built.
* As Chekov is already on the Enterprise when Kirk takes command, then we must assume that he must have taken a different position on the ship for what we see as season 1 of Star Tek TOS, that keeps him away from the camera. This also then fits in with Khan saying that he remembers Chekov from the Enterprise in Star Trek II, even though Chekov never actually appeared in "Space Seed" from TOS.
Those are the main ones I can think of, I'd be interested in listening to any other ideas that anybody has.