In what cases would a bitcoin address not have a private key? According to the https://en.bitcoin.it/wiki/Address site, it states that "most" addresses have a private key.  Here is the relavent text:


  Most addresses have a "private key"
  
  For most addresses, there is a corresponding secret number known as a private  key that is required to spend funds previously sent to an address.
  When using a Bitcoin client, private keys are typically stored in the wallet file. The private key has a special purpose - it is mathematically needed to create valid transactions that spend the funds originally sent to the address. If the private key to an address is lost (for example, in a hard drive crash, fire or other natural disaster), any associated Bitcoins are effectively lost forever.


I have always assumed that Bitcoin worked in such a way that all addresses must have a matching private key due to the public/private key encryption on which it is based.  In what cases would a bitcoin address not have a private key?
If an address merely 'looks like' an address and all other aspects of a transaction are ok then miners will include it in a block. 

This has been (ab)used to embed ASCII art into the blockchain at the cost of permanently destroying some bitcoin.

For an example with explanation see https://bitcointalk.org/index.php?topic=33618.msg420597#msg420597