Weak and Strong Collision Resistance, again
There are many situations where collision resistance is exactly the property that you need. For example, assume that I want to get a certificate from a CA with the URL www.google.com so that I can play a fishing attack against Google. Assume that I manage to find two certificates with the same hash; one has URL that is www.google.com and the other has something else (e.g., www.yehudalindell.com). Then, the CA will happily sign on the certificate for the latter URL, and due to the collision I will now have a valid certificate for google. Another example is code signing: if I can construct two pieces of code where one is malicious and the other is perfectly valid but both have the same hash, then I can get my valid code accepted to Apple Store or something like that, but then get people to download my malicious code.

It is really important to understand that birthday attacks on hash functions are just the generic way of finding collisions when nothing better is known. However, advanced cryptanalysis can do amazing things and find really valid collisions. For example, using advanced techniques and MD5 collisions, a rogue certificate signing certificate was obtained. The Flame virus also propagated by using an MD5 collision. So, this is not there, but reality!

Weak collision resistance, or more exactly, target resistance or 2nd-preimage resistance is important when a collision must be found with a given hash. But this is often not the case.