From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.
Concept No. 42: If you check the river, most players will bet only with very good hands and with bluffs. They'll check down hands that could win a showdown, but that are unlikely to be called by worse hands.
Yup. This is the correct way for your opponents to play the river, and since it's rather basic and intuitive, most players have mastered this strategy. You will see players deviate from this, but it is quite rare. However, I think it is worth noting because you don't want to fall into a pattern where you pay off your opponents if they make huge bets with hands that are only moderately strong.
As Sklansky and Malmuth point out in their discussion, this fact means that a lot of your medium-strength hands become "bluff-catchers." That is, they can only win if your opponent is bluffing. For example, it doesn't matter whether you hold top pair or bottom pair if your opponent will only value bet with two pair or better. Both hands can beat only bluffs. As S+M point out in Concept 44 (which I analyze below), the bigger your opponent's river bet, the less your hand matters; for example, if your opponent is rational and makes a bet of ten times the size of the pot, a wide range of your hands become "bluff-catchers," since your opponent will probably either have the nuts or nothing. On the other hand, if your opponent bets only one-tenth of the pot, the strength of your hand is very relevant.
Concept No. 43: Big bets mean big hands. Don't make or call big bets very often with weak hands.
As uncontroversial as this concept seems, I don't think it's precisely right. Big bets can mean not only big hands; they can also mean big draws or hands worried about draws. When your opponent makes a big bet (or when you make a big bet and get called), his hand range becomes much stronger. Thus, you should only call or make big bets with hands that have the potential to beat your opponent's strong range. This means you should be calling or making big bets only with big hands or big draws.
We can look back at some earlier concepts that touched on this topic to find some more exceptions and possibly gain some interesting insights.
Concept 35 seems to contradict this concept: "Unusually small bets tend to be made either with a big hand ... or with a bluff... With one pair your opponents will usually either check or bet a larger amount." So Concept 35 suggests: Big bets mean one pair.
Concept 40 also somewhat contradicts our current concept. This one suggests: Big bets mean the board has lots of likely draws.
Concept 1: "When in doubt, bet more" suggests: Big bets imply more doubt. Or something. This concept was pretty dumb.
To be fair, several concepts do support our current concept. For example, Concept 11 said "A big bet is the most relevant and accurate information available."
Concept 39 also supports our current concept. This was the one suggesting that you respect bigger bets more than smaller ones.
Concept No. 44: The bigger a bet your opponent makes, the more of your hands that turn into bluff catchers.
As I said above in my Concept 42 analysis, I agree with this one. At least in my games, my opponents are usually smart enough not to bet a huge amount with a hand that is only moderately strong, because they know I will probably only call them with hands that are even stronger.
It occurs to me that if my opponent is especially talented, he might be able to trick me into calling with a weaker hand trying to catch his bluff, but this is a very high-risk maneuver for him if his hand is only moderately strong.
I like to think about these concepts in terms of hand ranges, when possible. When my opponent makes a big bet, his hand range is polarized: usually he'll have near the nuts, sometimes he'll have nothing. My range falls almost entirely between these two poles, so my hands are mostly bluff-catchers. When my opponent makes a small bet, it's usually with a hand that is only somewhat strong, or it could be a bluff. Many of the hands in my range will fall on either side of his value-betting range, so my hand strength is the main factor determining how I react to his bet.