I'm sure this post is going to feel like a commercial and I'm fine with that. :)
A friend (who will remain entirely anonymous) posted a light-hearted jest on Facebook about some password requirements being insane and asking about ways to make up a password that worked within these particular criteria. All of the usual suggestions came up: take a normal password and change some letters to numbers, the algorithm that you remember that turns the url of the site into a password, XKCD's awesome method at http://xkcd.com/936/, and I mentioned LastPass. At this point I hadn't used LastPass, only heard about it and thought it would solve his problem.
LastPass is a secure password management tool that will generate (and remember) new passwords for anything you want. The passwords tend to look something like this "bQ0SCNPS7Q1c" and are encrypted and stored locally as well as on their servers so that you can access them from anywhere. Your master password is the key to unencrypt your other passwords. The entire service is free as long as you use their site and/or browser extensions but you can pay $12 a year to be able to access it from your mobile device and at that price why not.
During my research on the service I decided to create an account and begin using it, but not trusting it yet. I enjoyed not needing to remember several of my passwords and the security admin that lurks deep inside my brain kept telling me that this was a good thing. It wasn't until Twitter announced that they were requiring everyone to change their passwords because of a security breach that I really began to see why I loved LastPass. After the announcement, I gladly allowed LastPass to take over from there for just about everything.
Let me just say that I've been using LastPass for a couple months now and couldn't be more happy. After the Twitter incident, I didn't go out and immediately change all of my passwords to the cryptic ones that it generates but as the opportunity arose I would gladly allow it to provide me with a new one. This thing has made me not worry about my passwords anymore and when security holes rear their ugly head I don't feel too bad about having to change any of my passwords.
If you've every forgotten a password or had an account compromised then LassPass will certainly help you out. I couldn't recommend it with any higher praise and it's basically free.