It all depends on the reason one misses a flight, and the mercies of AA employees, who are often apt to interpret the AA Conditions of Carriage more liberally than they are written. (IMO, everyone who flies should be at least vaguely familiar with the specific airline's C of C - before even booking on them.)

Missed a connection because of weather? Reaccommodation, but it might take some time or rerouting, even on another airline (see the Unofficial Users Guide sticky about involuntary rerouting and receiving original routing / mileage credit.) Every attempt will be made to accommodate in the class of service purchased - and I have been "Rule 240'd" or "Rule 80'd" to other airlines when necessary, sometimes people may be opped up, sometimes the choice is not so good - but they will try, IME, as number_6 says. (Number 6! That IS impressive!)

SFO-ORD in winter is a great example of what can go wrong, yet that is a connection I am sometimes forced to use due to fares, available seats, etc. AA has rerouted me to SFO-LHR-xxx using BA in J cabin (even on a discounted fare,) SFO-LAX-LHR-xxx or SFO-JFK-xxx or SFO-DFW-xxx using AA in J cabin, etc. (To make their job easier, , I will generally try to keep abreast of what is happening, keep the EXP and other numbers in my cell phone and am quite willing to throw myself at the tender mercies of the Admrials Club AAngels when these things happen.) Nonetheless, not long ago bad DFW weather forced me to accept a downgrade on a domestic flight AND rerouting to a nearby city to avoid RON and >24 hours in DFW with full hotels. Masses of people, late international flights with connecting passengers, standby lists of >30, more nasty weather, no local rooms - not good augury!

Missed it because of bad weather or ground traffic getting to the airport? Anecdotally, they will attempt to reaccommodate you (see next post.) Missed it because your alarm clock didn't go off, you forgot to reset your clock to Daylight Savings or similar? They will, anecdotally here, still attempt to reaccommodate you. It will pay to be nice and cooperative in these instances - look at your actual recourse in the Detailed Fare Rules and Conditions of Carriage to see what the worst possible outcome might be.

But generally speaking for the latter, it is your obligation to be there before the various cutoff times (baggage check, check-in, gate cutoff, etc.) and technically, if you do not call to cancel or inform before departure, you are stuck with at best a change fee and the difference between your original fare conditions and the fares available, or at worst a worthless and valueless ticket and stuck for a way to get back - most likely, a full walk-up one way fare back, unless the ticket already was a pricey fully refundable unconditional one.