The importance of password security cannot be overstated. Password lists are stolen and sold every day. Right now, there are dozens of phishing emails sitting in my spam mail hoping to steal my passwords.
A secure password should consist of a seemingly random combination of letters (uppercase and lowercase), numbers and special characters. Longer is better, with eight being the acceptable minimum.
It's important to choose a different password every time you register at a new site. In the event that a site is compromised, you'll need only to change your password at that one site rather than at dozens of sites.
The best way to create and recall many different passwords is to create a master password mnemonic that can be altered for every site. Let's try an exercise.
Think of the chorus of your favorite song. For Michael Jackson's Thriller, the lyrics are "'Cause this is Thriller, Thriller Night." Taking only the first letter of each word (while retaining the case and special characters) we're left with 'CtiT,TN. The result is a seemingly random but easily remembered password.
Since every website we register for will require a unique password, we're going to expand on that original mnemonic by adding a unique identifier. If I were to register on dating site Plenty of Fish, I would use the same first-character methodology and append the password with !PoF resulting in 'CtiT,TN!PoF. Not only is the password unique and easily remembered, I've made it more secure by making it longer and adding another special character.