As I found out tonight, when compact fluorescent bulbs burn out, they do so in a rather spectacular fashion.
When the vacuum inside the tubes is lost, oxygen gets in, contacts the tungsten filament, and ignites, causing overheating. This isn't so different from the way in which an incandescent light bulb burns out. What is different is how the bulb flashes and pops alarmingly for several seconds, while releasing some acrid-smelling smoke.
After some quick searching, I found out that the smoke is caused by the epoxy that holds the bulb together overheating and starting to burn. Apparently, it's not a fire hazard, but holy crap, it smells bad.
Good thing it's a cool night in Houston - I'm airing the place out and getting some extra use out of my homebrew screen door.
One more important thing I learned_ You need to be very careful when screwing in your fluorescent bulbs. Apparently, the glass tubes are somewhat fragile, and you can easily cause structural weakness by applying too much pressure or knocking it around. So, you should never twist the bulb while holding the tube - always hold it by the base. This will help prevent early burnouts and ensure that you get the several years of life that are advertised.