We don't have too much to work with, hopefully Star Trek Into Darkness
will help change that, but I'll give it a try.
TNG: Some version of TNG probably happens. The Enterprise might look different and might even be more advanced but most of it should still be the same. The parts that could be different are the stories that involve the Klingons and the Romulans (depending on what the new films do with them) and the Borg, if they happen to appear earlier. In the new timeline there might not have been a battle at Nerendra III, depending upon how different the political situation is, and the "C" might've stayed in service right up until the "D" was commissioned.
DS9: The Prophets live in the past, present, and future. They're immune to changes in the timeline because they exist in all points everywhen. If linear reality changes around them, they'd still become instantly aware of what will happen because they're already there and they'll immediately have a new plan. Sisko would still exist or, if not, someone else from Earth -- or anywhere not of Bajor -- would still be created with the help of the Prophets. Said person will still go through a set of circumstances leading them to Bajor. Whether or not Wolf 359 would be what leads to it would be hard to say.
VOY: Would be the least affected. The Delta Quadrant is away from everything else that has happened, is happening, or will happen in the rest of Star Trek. At least until Starfleet is advanced enough to reach that quadrant on its own. For the sake of argument, let's say it wouldn't happen until a century after the series is set, as Q said in "Deathwish". I doubt New Trek will touch the Cardassians, so the Maquis situation wouldn't change.