I started using LastPass since last week. I never felt a need for such utility dedicated only for password management, given that the browsers remember them well.
Besides standard password saving across browsers and across machines, you can use it in a very useful way. With the Groklaw password leak, the danger of exposed passwords has become very clear. Although you don't care if someone logs into your comments account, if you use the same password everywhere, all those services are compromised.
You can solve this problem with LastPass. It's pain to remember a new password for every new service we sign up, that's why we tend to use same password everywhere. With LastPass installed, whenever you sign for new service, enter any string for password without fear for forgetting it, because LastPass will remember it for you.