How long do you look at a tactic puzzle before taking a hint?

I never take a hint. I didn't even know people do that.

Once I decide to give up, I pretend it's a real game, and calculate the line I think is best. Then I look at the solution.

I'd say nothing more than 10 minutes. Sure you might solve it after brute force calculation for 30 or 40 minutes. This can be a good calculation / visualization exercise, but it's a waste of time for tactics.

I would say when you're so lost, that you're about to just guess a move, then take a hint. 

Pretending that it's a real game though is a pretty good way to learn. But during a tactic, if I can't find the tactic, and know what I'll play in a real game, I'm still not going to play a move that I know isn't the solution. 

I guess that's because I mostly solve from books, not online.

Yeah, if you have an online rating, then go ahead and guess whatever crazy forcing move you couldn't quite calculate to the end.

No hint.  My guesses usually get me the first move and it's usually a little easier from there.

Yeah I don't use the hint either. Mostly because that basically means you got it wrong. It will say "solved with hint" and deduct points. I don't really care about tactics ratings, it's just practise after all, but no one likes getting the answer wrong lol. 

When I think castling is the answer, I know its time  

and that's only because I didn't see a tactic with casting as the right answer yet. maybe someone can tell why?

The problem is, there is a "perfect" move, or maybe the fastest move to victory.  However, I think there are often a lot of good moves that will lead to swift victory in some (not all) of the puzzles.  So it pisses me off a bit if I think my move is winning and it says "WRONG"

As bobby fischer said, the king is the thing!  the win is the thing imo