There are a few warning signs that point to a bad circuit breaker:
A burning smell near your electrical panel. This is a very urgent problem, so if you find such a smell, shut off the power and call an electrician ASAP.
Breakers that won't stay set. A breaker that re-trips as soon as you reset it is probably experiencing a short circuit, but it could be an issue with the breaker itself. If you can't find a short circuit issue, call an electrician to investigate.
Signs of burning or melting on wiring, breakers, or electrical outlets. Burning or melting are signs of overloaded circuits; if you see any signs of it, have an electrician come and take a look as soon as you can.
Breakers that trip often. Breakers that trip constantly may simply be overloaded, meaning you need to remove some electrical devices from that circuit. If you're fairly sure the breaker isn't overloaded but keeps tripping anyway, there may be another issue with the switch.
The breaker switch is loose. If your breaker switch flops back and forth between off and on, and doesn't firmly lock into both positions, there may be a mechanical issue with it. You should replace the breaker.
If you have a multimeter and you know how to use it, you can test each of your breaker switches to see that they've got the right amount of electricity running through them.