This is how I currently remember passwords to new accounts and some old ones that I hardly use: I write it all down on a notebook in a secret place in my work/office at home. Shhhh!
But there are other ways and I came across one today that works well for mobile warriors from WebWorker Daily . It involves using a password program called Password Safe for Windows and Password Gorilla for Mac, Windows, and Linux.
Heck, you can use those programs as it is if you're on one computer. However, if you're truly mobile and you travel quite a bit or work across different systems, there another step you'll need to take. So, using a password program is step one.
Step two: WebWorker Daily uses dropbox. Why? Because they encrypt the files you upload. Since these programs produce a password file, you can upload the file and access them with these password programs from anywhere you work. WWD also suggested using regular text file and let Dropbox's encryption protect you. I'm not so sure about that.
And that's it. It's quite simple after you set it up. I really like Dropbox too. It's cloud, something we haven't talked about in a while, and making sure you have access to your accounts wherever you are.
Note: I also use 1password as well on the iPhone and Mac.
Also read Joel On Software for info.