Three handed on the river. You have a huge monster hand (like a full house) and are 2nd to act. The first player bets into you. There are many cases where it's best to just call!! For example, if the first player is a nutty bluffer and his betting pattern tells you he likely has no hand at all, so he won't call if you raise. If you raise, the 3rd player will see a bet and a raise and be very scared and fold a lot of good hands. If you just call, however, he sees the bluffer jam and you call - that makes you hand look marginal, and the 3rd player may call or even raise with mediocre hands like top pair.
Three or more handed on the turn, you have the 2nd nuts but are afraid the first nuts is out. For example, maybe the board is a 4-flush and you have the K of suit, it's quite likely the A is out there but you're not sure. Another case would be if the board is two-paired (like 55TT) and you have the lower house. In both cases you're not afraid of any draws and you're either dominating or killed. You're first to act - you should check!!! If everyone checks through, or only a maniac bets and everyone else folds, you know your hand is very likely best. However, if you check and there's lots of action you can just dump your hand. On the other hand if you bet you could get a few calls and still have no idea if you're ahead. It's key here that you can't get outdrawn, and it's on the turn so if you miss value on the turn you can still get it on the river, and your hand is not big enough to bet the turn & river.