1) Do all cigars benefit from aging (assuming they are aged an appropriate amount of time for that cigar, i.e. not over-aged)?
In theory yes, but a very well aged crudy cigar is still a crudy cigar. Some smokes are better for aging than others although all good cigars should get better. If you are going to set cigars aside for aging I'd avoid cigars on the milder side of what you like now. You don't want something to mellow to less than you like and you are more likely to grow into stronger cigars with time anyway. Actualy, in many cases the difference between a premium and super premium cigar is mostly just the age of the leaf, so if you age your own smokes they should impove.
2) What, in general, is a good amount of time to age cigars (or is it more like wine in that every cigar is really different and requires different aging times before it truly comes into its own)?
The younger the tobacco the greater the benefit. Each cigar will get to a point where aging it further will not reap noticable changes. I've smoked cigars from the 1930's and older that were great smokes. I've also had cigars that were great when rolled that never got much better and now 15-20 years later are mellow to the point they only satisfy me early morning as a first cigar of the day.
3) What exactly is happening to the cigar during the aging process?
Nature Baby! Cigars are natural products and aging a cigar is a bit like a bueatiful compost heap, the leaves are going though changes, some of what it was born with like Tar, Nicotine, and Amonia are breaking down to make the cigar smoother and less bitter, other things like the esential oils that gives the cigar much of it's flavor are becoming more consentrated, and may even crystalize on the outer wrapper of the cigar as little flavor bombs we call plume.
In general with time the bad parts of the cigar get less with time while most of the good parts stick around, although they may change.
Best plan is when you get those sticks that are too full or don't do it for you right now, stick them back a year and give them another shot then. You may not come to love them, but they will be a different cigar after a year for sure.
As for over aging, most cigars can handle ten years no noticable drop in strength, many vintage cigar guys consider anything less then 20 years still developing and I've had some great cigars that were close to 100 years old that I loved, doubt I would have wanted to smoke one when they were new though, I bet they were very very strong back in the day.
