What is a block withholding attack? How can a block withholding attack be performed, what would be its purpose and who is it a danger to?

Edit: when I posted this I was thinking about withholding a block you mined in a pool. But withholding blocks can form the basis for many different attacks. I think this is still useful as a broad question. It is a central concept in bitcoin security.
The simplest form of it called Finney attack, named for Hal Finney who first described it. The attack is variation of a double-spend attack involving accepting 0-confirmation transactions.

An attacker would generate a valid block but will not broadcast it, and then broadcast transaction A as a payment for a good or service. A merchant will see transaction A with nothing conflicting with it and accept the 0-confirmation transaction. Right after that the attacker would broadcast the generated block with transaction B which will conflict with transaction A, the Bitcoin network will accept his block and invalidate transaction A.

The attack is quite costly because there is a time gap between generation of the block by the attacker and completing transaction A, during which someone else on the network could generate a valid block and broadcast it, thus invalidating the valid block generated by attacker. Therefore it is practical only if the merchant sells the product online and it could be release immediately, e.g. a key for a software product.

A general form of this attack was described by Satoshi Nakamoto: White Paper, section 11. In theory, an attacker could pre-generate any number of blocks, e.g. if a merchant requires 1 confirmation before releasing a product an attacker would pre-generate 2 blocks ahead of the network and only then broadcast transaction A to double spend. But with each block the cost increases exponentially, and the practice of accepting 6 confirmations before releasing the purchase makes this attack possible only in case where the attacker has close to 50% of network hash rate or more.