I greatly over-simplified the algorithm in my initial post, but there are advantages to a straight hash of the password.
Even if you can intercept the person's hash and login to that site, you still don't know the user's original plaintext password. A lot of people re-use the same password throughout many (or all) of their online accounts. The attacker may be able to impersonate the user for the current site, but they don't have their actual password to gain access to other sites.
What I was talking about in my original post (but didn't properly explain) was using hashing as part of a larger algorithm for doing a challenge/response login. The idea is explained here: http://pajhome.org.uk/crypt/md5/auth.html
I agree that HTTPS is the way to go if security is a huge concern (like for banks), but for a simpler site you could get away with using CHAP and still provide a reasonable level of security.