You can enable your computer to automatically ask to "remember" all your passwords, which is what I do. Then, you can access your saved list in the security settings (it is different on a PC than a Mac and I've just recently fully switched to Mac, but it's located in the Internet Options on a PC). I also tend to use the same password for all sites and change ALL of them every 72 days or so. I'm sure it isn't as secure, but for now, it is what I do.
Unfortunately, my PC laptop just died, and with it, all my saved passwords. As I go back and get the "reminder email" from each site, I too am creating a list in a document and saving it in my dropbox. My biggest problem lies in the rules regarding different symbols or requirements for passwords. When my "catch all" password does not adhere to rules, I forget it easily.
I have also created a folder in my email for all the "password reminder" emails, so I'm thrice backed up. Amazing how hackers can break in even when we can't seem to access our own stuff!