Some schools are part of the Council of Graduate Schools (CGS), which has rules about the April 15th deadline.
"Acceptance of an offer of financial aid (such as graduate scholarship, fellowship, traineeship, or assistantship) for the next academic year by an actual prospective graduate student completes an agreement which both student and graduate school expect to honor. In those instances in which the student accepts the offer before April 15 and subsequently desires to withdraw, the student may submit in writing a resignation of the appointment at any time through April 15. However, an acceptance given or left in force after April 15 commits the student not to accept another offer without first obtaining a written release from the institution to which a commitment has been made. Similarly, an offer by an institution after April 15 is conditional on presentation by the student of the written release from any previously accepted offer. "
So, you can withdraw your acceptance of an offer without penalty through April 15th. After April 15th, if you have accepted an offer from any school that is a member of the CGS, you will have to get a formal written release from that school before being able to withdraw.
For a list of the CGS schools, go here:
http://www.cgsnet.org/portals/0/pdf/CGS ... ch2009.pdf
Hope that helps! Best of luck!