As a tank on my main, I groan when thinking of entering Raid Finder, mainly because of the wait. There are only two tank roles, after all. With the new loot specialization coming to 5.3, players looking to win tank gear have hope of a less painful wait in a DPS role, at least. Even if you're used to the long wait, everyone has a limit. I remember waiting as a tank in a Raid Finder queue for an hour and forty minutes. I'm not usually willing to wait that long. I'm relatively comfortable with waiting about thirty to forty minutes before moving on.
When it comes to PUGs, I'm quite patient, usually waiting longer than I probably should. In a PUG, I tend to have a personal connection to at least one of the other players in the group, so I'm not quick to leave.
How long are you willing to wait, whether it be for a dungeon, Raid Finder, battleground, or a PUG? While in queue, how do you pass the time? I usually find myself completing dailies or battling pets. But at what point do you throw up your hands and leave?