One of the best times to check raise is when you are out of position on a paired flop. Having a hand like Kh9h in the sb and defending against the button raise, you see a flop of 477 rainbow.
This is a good spot to check raise, since you can so easily rep a 7 with hands like 78s,76s,A7,78o,67o and if the player on the button has big cards, he has not hit the flop. Even if he/she is holding big over cards like AK, it's hard for them to call cause if you have a 7, they are only drawing to runner runner outs. So they are thinking, "even if I hit an Ace or King on the turn, will my hand be anygood? how big of a bet will I have to call on the turn ? "
Generally paired boards a good situations to check-raise, but try to avoid doing so vs. really tight opponents as they will likely have a hand that can call. Also more experienced players will often float here and try to steal on the turn.