What are the failure mechanisms in an integrated circuit?
Two immediate modes of failure are over-voltage and over-current.   


If you have a high impedance input like a gate to a mosfet, then high voltage (even at very low current) will cause a puncture in the capacitive gate of the mosfet as the electrons have enough energy to cause the dielectric to breakdown. Once this occurs, the resistance of the input drops to near nothing and a later low-voltage high-current will further heat up and destroy the mosfet. This mode of failure is why there is ESD protection on many chips.   
Over-current causes over heating of the device. Once temperatures get high enough to start changing the structure and/or burning of the internal semiconductors, it will start acting funny, working less efficiently, or completely failing as an open or short.


It's possible that you could think of reverse voltage as another failure mechanism, but generally that still falls under one of the other two categories, it's just different to think about. For instance, if someone reverses a power supply on a circuit with a diode in it, they may expect no current through the diode and instead get an over-current condition because the diode would now be forward biased.

Note that capacitors, resistors and inductors (and any other circuit element) are likely to be damaged in similar ways as transistor ICs, i.e. over-current and/or over-voltage.

Other failure modes of electronics in general may be found here:
http://en.wikipedia.org/wiki/Failure_modes_of_electronics