Thoughts from a reflective educator.
I'm using the following xkcd comic to help the teachers at my school with their password selection.
There is also a very useful script, created by Steve Gibson, available to test how long it would take a brute force attack to figure out your password with a computer. While I don't recommend entering any actual passwords you intend to use into an password strength checker (there aren't that many websites out there, so an hacker could easily steal the passwords you enter into their "password" checker and try them all over the place, thanks to @drdouggreen for the reminder), this can be an excellent way to experiment with different types of passwords.
I also recommend reading this post I wrote about how to change your password for every service you use, without having to memorize a new password for each of them.
As suggested above, we've spent many years training people to use complicated passwords which are actually not all that secure, when instead, you can use a longer, much easier to remember, password that is much more secure.
David is a mathematics teacher and a learning specialist for technology at Stratford Hall in Vancouver, BC. He has been teaching since 2002, and has worked in Brooklyn, London, and Bangkok before moving back to Canada. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.