Make Every Card Count
Try to make sure every card you lay down is working toward bettering one of your own rows and blocking one of your opponent's columns. In the examples below, you are playing columns, your opponent is playing rows.
Figure 1: This play appears to be safe because the card is laid in neutral territory, however, this play is allowing your opponent to seize two plays in a row while you essentially passed on yours.
Figure 2: This play is clearly better because you just obtained 2 points for the 15 count and you're also setting yourself up for a potential run.
Figure 3: This is your optimal play because you have bettered your hand, as noted by figure 2, and you are lessening your opponent's opportunity to get a double run in their raw by blocking.
Go for Big Hands
When there is only one space left in a hand that has high scoring potential, it's a good strategy to try to complete the hand before your opponent blocks it.
One way to do this is to send a non-scoring card to the crib if you have not already done so. You are then allowed to immediately turn over another card, in hopes of completing the hand.
Pay attention to your crib card and the cut card
Take note of the cut card when discarding to the crib. For example, if the cut card is a 7, you would want to discard an 8 toward your own crib, but not toward your opponent's crib.
Mind your Fives, Sevens, and Eights
The 5 is the most valuable card. The chance of scoring a 15 with two cards is four times greater with the 5 than any other card. This is because it can be combined with the sixteen 10-count cards.
The largest hand possible, the "Perfect Hand", is comprised of four 5s and His Knobs.
Quadruple runs built around fives, sevens, and eights are the most common high scoring hands.
Whenever you play one of these three cards you should take extra consideration to make sure you're allowing yourself the most opportunity to build off them, at the same time limiting your opponent's opportunities.