My favorite security tips are below. This is not a comrehensive list!
Passwords have been exposed from dozens of major websites, including LinkedIn, Gmail, and MySpace. If you use the same password on multiple sites, a hacker can access your other accounts just by hacking into one website.
Password managers make it easy to never use the same password twice by generating random passwords, auto-filling usernames and passwords, and keeping all of the passwords encrypted using your complex master password.
Take the time to choose and learn a password manager, and start moving all of your passwords into it.
A complex sentence or 3-4 random words put together make human-friendly passwords that are hard for computers to crack. Toss some capital letters, numbers, and punctuation in for good measure.
Whether it is your operating system or your websites, security updates are a good idea. After all, they are released when a security vulnerability is found. Not installing them means you are leaving an open door.