There are two levels:
You need some hashing as a second line of defence, so that what you store on the server (I call "server" the system which does the authentication by verifying a given password) is not sufficient to actually impersonate users. This avoids escalation of a partial, read-only breach (e.g. stolen backup tape) into a more complete, read-write access. See this blog post for a longer discussion.
If you hash the password, then you may need to use a password hashing function if the source password has low entropy. Passwords chosen by human users have low entropy. If you generate the passwords "randomly" then you may obtain high-entropy passwords. Or not. The good point of generating passwords through a known, systematic process that feeds on a cryptographically secure PRNG is that you can compute the entropy, instead of merely estimating it. However, you must still make sure that you get enough of it.
For instance, if you generate a password as a sequence of 10 random characters (lowercase and uppercase letters, and digits), and all characters are chosen uniformly and independently of each other, then there are 6210 possible passwords and each of them has the same probability of being chosen than any other. Entropy is then equal to log(6210) (base-2 logarithm), i.e. 59.54 bits. That's not bad, but possibly still a bit too low for comfort if a simple hash function is used, since a good GPU can run billions of MD5 or SHA-1 per second. You should then add salts and iteration, i.e. use bcrypt (but a small iteration count would already be fine).
If your passwords have at least 80 bits of entropy, then you can consider that they are strong enough to defeat even rich and determinate attackers, and you can use a simple hashing (i.e. you can get away with a simple hash call and also with not using salts). With random letters-and-digits, this translates to 14 characters. I insist that this is true only if the 14 characters are chosen randomly, uniformly, and independently of each other. These are requirements that you can fulfil with your password generator, but you cannot realistically expect them from a user-chosen password.