Jcjchung and Serfty - these connections seem VERY tight for MIA on a Sunday especially. Everything seems to run slower in MIA for logistics (baggage, ticketing, immigration esp for non US citizens) than most other AA hubs. Perhaps a bit of "latin time" is going on. Normally I would say that 2 hours would be tight for a non- US citizen with checked bags, but on a sunday things are very busy - even worse in the afternoon.
As someone else posted, you can probably relax and don't worry too much because if you miss your connection your status should have them take care of your reservation and book you on the next flight. You noted that you were going to the "Carribean" but didn't say where. Many islands have several fights per day, but some of the smaller ones may only have 1 or 2 on AA metal. Hopefully things will work out.
For Serfty heading to DFW, your connection being in the afternoon on a Sunday and with even less than a 2 hour window will be tight if you have a checked bag and not a US citizen. The good news is that there is a 6:50 MIA-DFW flight, and worst case the last flight between MIA and DFW leaves at 840pm. If DFW is you final destination, you'll probably get there for sure Sunday. If you have connections from DFW, unless they're west coast, you may have problems if you dont get on your scheduled flight.
Marc