We've all seen it. Four players see the flop in an unraised pot. The turn appears to help no one but it hasn't helped you either. Everyone checks around again and there you sit in late position. No one seems to want this pot but it's going to cost you a big bet just to win two. Is it worth it? Maybe someone is scared to bet that bottom pair and has you beat. Maybe someone is slowplaying a big pocket pair. Maybe a lot of things.
The orphan pot can be a nice way to win some money, or a sad way to lose some. The pots are so small that you will have to take them down 40% of the time to be profitable. That's a pretty high win percentage but these pots are a unique sort of beast. Win that 40% and you will make your 2BB/100. lose it and you'll slowly bleed your bankroll.
As with most plays the more you know about your opponents the better your odds of success. If it's to early to have a read on the players and your in late position when this situation arises. Take a stab at it. If you get a call be prepared to fold the river and if your raised just let it go. It may have cost you a big bet but you've gained some insight into that particular player.
The only time that it really doesn't make any sense to even try this play is when you have a player who almost infallibly slow plays his big pocket pair. This player usually waits for someone to bet into a pot and then check-raises. Just check it around against this type of player. If he/she still checks the river then you may want to try it. I emphasize may because just about any player with an A will call you in this situation. You should have an A with a big kicker before even considering this play on the river.
All this may seem elementary to you but just think back at all the times you've seen this come up and nobody bets till the river, if they bet it at all. The orphan pot is called that for a reason and often the first player willing to adopt it gets to take it home.