About 2 years ago I switched to
LastPass and I absolutely love it. Firefox no longer saves my passwords. Some people don't like that your passwords are stored at LastPass, but it syncs all my passwords between all computers, laptops, netbooks without any hassle. I now have long random generated passwords different for every site... no more using an easy one for all forums, one long one for online stores, etc.
Just make sure your LastPass password is something long and secure with random numbers and symbols that you can remember. Also make sure the email account associated with LastPass has an equally difficult password. If they can hack your email, they can request a password change if they can get access to your email.
LastPass is free, but there is a pay version which I think the main difference is that it will also sync with your phone, or let you also password some programs on your PC. The free version is more than enough for me.
KeePass is another excellent free program that doesn't store anything in the cloud, so I occasionally use it for passwording programs like CuteFTP so my ftp passwords aren't easily accessible to hackers. I don't think it does near as good a job for website passwords though as LastPass.