[dayman]

With a new gun I usually put 200 through it to test it's reliability, and to get use to it. If there are no flaws, I put a box of my carry ammo through it, and if there are no flaws I assume it's good to go.
I have a range at the house, so I tend to shoot frequently but not a lot of rounds in any one session. So, 200 rounds out of a given gun generally takes a couple weeks.

I shoot all my guns fairly regularly, and practice clearing drills. Also, I find cleaning my guns as cathartic as shooting them, so I clean them pretty regularly. So, since any gun I'm carrying going to been fired and cleaned fairly recently, I'm unconcerned with my guns passing any sort of a marathon torture test.
However, I pretty much only buy well-researched, new guns from quality manufactures. IMO 200 rounds is enough to determine if I've gotten a lemon, and 20 rounds should be enough to discover an ammo problem.
If I were buying used, or buying from a hit-or-miss company, I might extend the testing.

If a gun does fail I generally try to identify the source of the problem and fix it. It's never actually happened, but if I couldn't identify the problem I'd probably chalk it up to gremlins, and start over with the 200 rounds.

I don't think there's one right answer though. Just test until you feel comfortable trusting it.