If two websites use this scheme and they both get hacked and a user has an account on both with the same username/password the attacker has to do half as much work. Another reason is an attacker can compute a rainbow table prior to getting access to the hashed passwords. This would reduce the amount of time the owners of the site would have to respond in the event of a breach. Finally, it's really easy and cheap to generate a random salt.

You can, but it prevents you from allowing changing the username (which might be fine, but why tie yourself?) and it provides less entropy - a username + password can be small enough to fit in a rainbow table, while a random salt can have whatever size you want.

Excellent explanation. I'll further this by adding that, in my use of the excellent PBKDF2.NET library, I generate a salt with the same number of bits that the hashing algorithm generates (e.g., 256-bit salt for SHA256). I can't remember where I read that this was a good practice, though. :(