How long can an average submarine stay under water?

Modern nuclear submarines can stay underwater indefinitely; it's only the limitations of the crew (food and supplies) and mission requirements that dictate mission periods.

As an example, my own personal longest time submerged is 72 days; one of my closest friends was on the USS Parche, at that time a SpecOps development boat out of San Francisco, and their typical missions were 120 days, with no port stops. Still another friend was on the USS Seahorse during their global circumnavigation mission in the early 80's; 180 days at sea submerged, with only 2 port stops, Diego Garcia, and Perth, Australia.

After about 2 months, if you're not able to ventilate at periscope depth due to mission constraints, the air gets pretty stale (even though it's constantly cleaned and recycled) and everyone starts getting a little testy, but that's normal when you're placed in close quarters in a high stress environment for long periods.