When an airline makes a significant change to your flight (what's "significant" varies by airline but can be as little as 90 minutes) you have the right to a) an full refund or b) to ask to be put on a different flight (without a change fee, and often without having to pay more if the new flight is more expensive).
Do airlines have to compensate for changing flights?
According to the law, financial compensation must be paid for changes for which the customer is informed less than 14 days before the scheduled departure time.
Does American Airlines give compensation for delayed flights?
If your flight was delayed or canceled and you don't accept our alternative arrangements, or none were available, we'll refund the remaining ticket value and any optional fees according to our involuntary refunds policy. Beyond that, we have no further contractual obligation.