In bridge, what are exceptions to "third hand high?"
It usually depends on the whole hand, but the typical cases where you don't play third hand high relate to communication/entry issues like keeping the communication between the two hands, creating/denying entries, messing up the entry timing etc.

Here is a classic example where the purpose is to deny an entry:

QJx
KQJTxx
xx
xx
          KT9xx
          Axx
          xxx
          xx
Axx
xx
AKxx
AKxx


Declarer (South) is in 3NT and partner leads a high spade and declarer plays the Q.

It would be a mistake to cover with the K. Declarer can then win the A, knock out the heart A, and enjoy overtricks.

If you duck, you are giving declarer the spade trick early, and forcing him to use the entry to dummy, before hearts are established.

Now when declarer plays hearts, you can duck once and cut him off from dummy.

Of course, declarer made a mistake by playing the Q! He should play low, and win the A. Now he has a sure entry in the form of QJ of spades, which he can use, after he knocks out the heart A.

Here is an example of maintaining communication between the two hands.

QJx
KQJTxx
xx
Qx
          AKTxx
          xxx
          xxx
          xx
xxx
xx
AKxx
AKJx


Declarer (south) is in 3NT, and partner leads the spade 9 (probably from 9x). Declarer plays the Q from dummy and you must let it win. The purpose here is to ensure that partner has a spade (i.e. maintaining communication) when he gets in with the heart A. When he wins the heart A, he can lead a spade and you can cash your four spade tricks, setting the contract. Notice that this is quite similar to ducking plays by declarer where he needs to duck early in order to establish suit and maintain communication with the dummy.