I have been using KeePass 2 for passwords. It's a free password manager and generator. You can enter your own password if you wish, but I let it make one for me.
For any banking sites, etc. I always enter my user name and password. I never choose to have my browser remember it. It's only a minor nuisance to open KeePass and go to the info for the site, then copy and paste the password to the page in question.
When you close the program, the info is encrypted, so, really, the only password you need to remember is the password to unlock your KeePass data. And you do have to remember that one, cause if you forget it, you're lost.
This might not be for everyone, but it works for me.