What types of cigars will age well? (I'm not talking about the few months apperently required, in an ideal world, of any cigar, but of the long term aging, of at least a few years)?
As you are talking about years, decades and more most of the worldwide experience is in aging Cuban Cigars because Non-Cuban cigars haven't been around nearly as long and the production techniques are so different. NC's cure and age loose tobacco fro several years and then roll where as Cuban leaf is cured and rolled. Most Cubans age well, some would say even require aging. Although the changes in processing over the last 10 years in Cuban production have changed things considerably if you ask me. That said some NC's do age well. Many, myself included have had good luck with aging Padron's and Fuentes (Opus and Anejos specifically). As for Cubans many will let them age at least a year or two before even trying. In the end some like em fresh others like them aged. It really is personal prefference and it's fun to find out what you like, provided you can keep you hands off them. The easy way though is to pay for aged cigars. There are sources that you can buy from with 10 years or more already in aging.
I have read about some cigars losing all their flavour if they are aged too much, so what doesn't age well?
This is possible with any cigar really. And it is really dependent on the long term conditions. I have had the opportunity several times to smoke the same aged cigars and had bland and fantastic ones, even when the fantastic one was actually older. There are lots of variables and I personally don't subscribe to the theory that any one particular brand or vitola will not age well. And given that you could safely, IMO, say that a Cuban cigar will not loose anything with 5, maybe even 10 years of age it's going to be a while, maybe never that I ever find that out.
Finally, because a coolidor doesn't breathe, some say that it can't be used to age cigars. Any truth to that?
Sounds like total bunk to me. Many of the vastly more experienced smokers than myself use vacumm sealing for long term aging. Even the English, the originators of the aging idea, used to seal individual boxes with wax paper for long term storage, read 20+ years. Now lack of air may slow the process down, but are you truly not going to open a cooler for 10+ years? More likely it will be opened every 6 months at the longest, and really should be to inspect your investment. That will provide an instant air exchange, removing the idea of no breathing.