Propane-fueled generators (mostly Onans and Kohlers) are quite common in travel trailers (which already have propane tanks, but no gasoline tank). They have a pretty good reputation for reliability, but as others have mentioned, produce slightly less AC power than their gasoline-fueled counterparts. Propane burns much cleaner than gasoline or diesel, which means that the engine runs longer between tuneups and oil changes.
Propane can be stored almost indefinately. Also, it doesn't produce varnish, which means you don't have to drain the carburetor bowl before putting the generator into storage. For these reasons alone, it's definitely worth consideration for a SHTF generator – as long as you've also got plenty of propane stored up.
Yet another option is a dual-fuel generator that can run on both propane and natural gas. This allows you to hook the generator up to your local utility's natural gas supply, yet be able to run on propane if the natural gas supply fails during an emergency (which is very possible).