It depends. But for comedy, as soon as I hear a laugh track, I’m outta there. I’ve lost my tolerance for it.
It sometimes takes upwards of half a season for the writers and actors to really know what their characters are all about. If the first few episodes aren’t actually very good but the show seems to hold promise, I’ll give them about that long. I won’t necessarily watch every episode but I’ll check in from time to time. If things aren’t clicking by halfway through the first season, they probably never will. If memory serves, good series that took about half a season to get up to steam include Star Trek: The Next Generation and Cheers.
Of course if the first episode is downright bad and shows no promise for improvement, I won’t bother with a second episode.
One of TV’s steadfast rules is that you can’t judge a show by its pilot*, so if the pilot has any redeeming qualities at all, I try to watch an additional episode or two just to give it a fair chance.
*Exception: NewsRadio hit the ground running and just got better from there, at least until the death of Phil Hartman.
3-5 shows, but that’s a bit misleading. In my situation (no cable, crappy DSL ergo no streaming, not enough OTA channels available here [river valley in the middle of Greater Podunk] to make an antenna worth the hassle), by the time I start watching a show, I already have a pretty good idea that I’ll like it (from recommendations and reviews) and a pretty substantial investment (either in optical discs or downloading-via-crappy-DSL), so the chances of me quitting any earlier than that are pretty slim. If I’m watching a new-to-me show, there’s a reason for it; serendipitous “Hey, that looks interesting, I’ll give it a shot” explorations aren’t on the menu.