I know that all of them say they must have an answer on the 1st of April, but when do they typically come out?
For many institutions, the last week of March (in 2015, I’d wager 27 March will be a popular decision-release date).
@TopTier When do the earlier ones come out?
That varies by school. I just found out UMich releases their acceptances in batches (like rolling admission). You would need to call each school to find out or check their web sites.
To clarify, a lot of schools require an answer by May 1st, not April 1st. A lot of the Ivies come out on April 1st I believe.