Desktop software KeePass password manager securely saves passwords to web sites, computers, networks, email accounts and banking applications on your computer.
Here's how it works: you set one master password which opens your KeePass password database. Once you're in, enter and retrieve usernames and passwords (with optional URL and notes) for various login services (ie, Amazon.com, PayPal, Ebay). KeePass can suggest hard-to-guess random passwords as you set up new login accounts, and it's small enough to save on a thumb drive so you can take your passwords with you. Because no one has your KeePass master password, it's very difficult for someone to open the database if your thumb drive or laptop is lost or stolen.
Before you download and install KeePass, though, a few things to keep in mind:
ONLY install KeePass on a computer you control and own. In other words, don't set up your password database on the office computer.
In general, the best place to keep passwords is in your head. But, it's a good idea to have a different password for each service you log into, so if Someone Bad knows one of your passwords, they can't log in as you into everything else. So KeePass is a good way to keep track of the different passwords, HOWEVER, it's not a great idea to rely on software (or monitor sticky notes) for important high-security passwords.
Never, ever give away your KeePass master database password. Yes, if you're suddenly struck with amnesia, you're screwed, but if you were trying to remember all your passwords instead of just the one master, you'd be screwed anyway.
The best passwords are easy to remember and hard to guess. See Pick a good password part 1 and part 2 for some hints.
That all said, KeePass is a good option to keep track of your medium to low security passwords - like to Amazon, Flickr or AIM. KeePass is free, open source, Windows only.