KeePass
http://www.keepass.info
I have yet to see anything as good as this, and the remarkable thing is it's free.
I can take it with me everywhere, and there are compatible KeePass programs (made by third-parties) that can open KeePass databases on phones (see the site for links), so you're never without your passwords. I still use version 1.x of KeePass for the PC since nearly all third-party KeePass programs are compatible with version 1 KeePass databases.
The phrase 'must-have' is used too loosely these days, but for me this is what defines it.
Too many features to list, some which only became evident with long-term use. I cannot live without it. And your passwords are not stored on some third-party server 'managing them' for you.