The first decision you will make each round of Cribbage is what two cards to discard to the crib. If you are the non-dealer, you want to leave your opponent as weak a crib as possible. This means not discarding two cards likely to turn into lots of points for your opponent.
Points to Consider When It Is Your Opponent's Crib
The most obvious thing to avoid, unless absolutely necessary, is throwing your opponent two cards worth points together.
This either comes in the form of a pair or two cards that total fifteen. Either of these is a dangerous throw into an opposing crib, not only because it's a guaranteed two points for your opponent, but because depending on the opposing discard and the cut-card, those two points could quickly balloon into 6, 12, or even worse.
Don't throw 5s into the crib.
Roughly 30 percent of the cards in the deck (all face cards, 10s, and other 5s) are worth two points when paired with a 5. Throwing a 5 into the crib, therefore, gives your opponent very high odds of scoring points from either his own crib discards or the cut card in conjunction with your 5.
For similar reasons, you generally want to avoid throwing two cards adding to five, such as 4, A.
This is doubly true of 2, 3, which not only add up to five but also are consecutive cards giving your opponent the opportunity for an easy three-point run. Generally speaking, throwing two consecutive cards should be avoided when possible for this reason, but some combinations are more dangerous than others.
6, 7 or 8, 9 are among the most dangerous consecutive cards to throw.
This is true because a single 8 or 7 (respectively) will transform them into five points for your opponent (a fifteen and a run), and if either of the other two cards also adds points, the hand can quickly balloon. If you must toss consecutive cards, try to minimize the damage a single card could do. One strategy is to throw A, 2 or K, Q since only a single card (rather than two) can turn it into a run, and only a 3-point run at that.
Of course, the best thing to throw to your opponent's crib is two cards that don't work together at all.
No pairs, no adding to fifteen or five, no consecutive cards, and ideally not two cards of the same suit. Throwing two low cards (e.g. 2, 4) or a low and middle card (e.g. 3, 8) increases the chances that your opponent can add some cards to your cards to reach fifteen. Throwing at least one ten with the other card as six or higher (e.g. Q, 7) means that your opponent will only score a fifteen if they manage to match with those cards since they can't use both in a single fifteen. Throwing two tens is often a reasonable idea, but if doing so try to throw 10, K, as any other combination gives your opponent a decent chance of a run if also discarding face cards.
As a general rule, it's not worth destroying a good hand to prevent a good crib.
If you can guarantee yourself a strong hand, your throw may give your opponent a strong crib, but may not. You're better off sticking with the definite. All else being equal, saving a low card for the counting round can be useful.
Finally, pay attention to the scoreboard.
Are you within a few points of winning? Throw your opponent a pair of fives if it will let you peg out during your hand before he scores. Conversely, if your opponent is close to pegging out, it may be worth throwing defensively to give your opponent the worst two crib cards possible (e.g. 10,K, which is usually worthless without a 5).