[Cryptography] hash size

[jamesd at echeque.com]

What does a 256 bit hash get you that a 128 bit hash does not get you?

What attacks could be done on a 128 bit has that could not be done on a 
256 bit hash?

With 128 bits, a birthday attack is just barely possible, in that 
someone could search 2^64 examples, but, supposing you don't care about 
birthday attacks, only about someone finding a pre-image or finding a 
new value that gives the same hash as someone else's hash, what do you get?