The final death of a black hole What are the different death scenarios for a black hole?  I know they can evaporate through Hawking radiation - but is there any other way?  What if you just kept shoveling more and more mass and energy into the black hole?
 A: If you shovel lots of mass and energy into a black hole, you will most likely get a bigger black hole.  It will not get indigestion, and it will not explode due to being full.  You may get accretion and jets if your shoveling is suitably generic.
Any list of possible "final death" scenarios will depend on your threshold for improbable events, and possibly which theory of quantum gravity you choose to accept.  Hawking radiation appears to be a fairly random process, and there is a very small but nontrivial probability for a black hole to destroy itself with a spontaneous eruption of big chunks of matter and energy.  The far more likely scenario seems to be that the temperature (and hence the flux from the radiation) increases steadily as the mass of the black hole decreases, until there is a very small hot black hole whose behavior can't be described well with semi-classical methods.
(This paragraph is very speculative, and may not reflect expert opinion.)  It seems possible to me that a collapsing body can form an apparent horizon (with respect to distant observers), and not collapse to form a singularity.  The final death may just be that it emits Hawking radiation until the radius crosses some threshold and the horizon disappears to reveal a dense macroscopic object made of matter.
A: Hawking radiation is a very slow process of the black hole losing energy and shrinking. If you counter this by supplying a little bit of matter or energy falling into the black hole you can easily overcome it and sustain the black hole. 
Other than Hawking radiation I don't think there is any known process for black holes to shrink. The area theorem in classical general relativity states that the area of black hole horizon always increases in any physical process. So at least classically there is no way for black holes to die, or even shrink a little. Hawking radiation evades that because it is a quantum  process (which is also why it is a slow process). 
As for the final stage of the evaporation, I think the honest answer is nobody knows. The logical possibilities are either the black hole shrinks to nothing and disappears, or it leaves behind some long-lived "remnant". Either one of this possibilities has its strong and weak points, but ultimately you'd need to know more about a quantum theory of gravity to know for sure.
A: A black hole with an event horizon that is thermally equal to its environment will not be in equilibrium.  A black hole with the mass of about the moon and in free space would have the same temperature as the CMB. If it absorbs a unit of energy its horizon increases in size and it become cooler.  This means it will preferentially grow.  If it emits a quantum of Hawking radiation it will becomes smaller and preferentially radiates more radiation.  So there is no equilibrium.  This is because the effective heat capacity of an event horizon is negative.  
There is no physically possible way to hold a black hole in an eternal state, except for one case.  This is a black hole in an anti de Sitter spacetime.  In this case the geodesic of the AdS are “repelling,” or equivalently any clock observed close to the boundary is seen to demark time at a faster rate.  So the BH will not crash into the boundary.  Also the Hawking radiation emitted by the BH will reach equilibrium with the AdS.  This is one reason researchers are so interested in AdS spacetimes.  
Around $10^{50}$ years from now there will be within regions bounded by cosmological horizons large galactic BHs.  The temperature of the horizon by Hawking-Gibbon radiation will be lower than the horizon temperature.  As a result these BHs will quantum radiate away so that around $10^{100}$ years into the future they evaporate away in a final flash of radiation.
A: Well, you could merge it with another black hole, so that is a way of reducing the total number of black holes in the universe, but I'm not sure you would call that "death."
It may also be possible to accelerate its evaporation by distorting its surface via tidal interactions with a nearby object, such as a fly-by of an unbound black hole, but all the radiated gravitational wave energy might just come from the tidal energy and not the initial BH mass. 
Choptuik and Christodoulou both showed that you could create a naked singularity by the collapse of a very special scalar field, but I don't know what its fate would be.
A: As you mentioned, it could evaporate away by Hawking radiation. We don't know how this ends for sure but it is most likely that it ends in a shower of elementary particles.
The second possibility is that it keeps growing because matter or radiation keeps falling in. It could even reach a thermal equilibrium with its own radiation if held inside a heat proof box. Over very long time scales this scenario might not be viable because matter may decay and be dispersed by the universes expansion so that the black hole has to evaporate away.
A third possibility is that it ends its life by falling into another black hole. The fate of that black hole then has the same possibilities.
There might be other ways a black hole could end that we don't really know about because we don't have all the theories. E.g. it might be possible for a black hole to be wiped out by a decay of the vacuum. It might also be possible for it to fall into a wormhole and pass into another universe. Perhaps in the other universe times arrow points the other way and it mutates into a white hole. I'm not saying these things can happen, we just don't know enough physics to say whether they can or not.
And don't forget that it can become a quantum supposition of different states that suffer different fates.
