I personally play World of Warcraft and have seen many others who do get real concerned about security lately. Stealing WoW accounts is almost an industry in itself now and certain precautions have to be taken. Here's a good list to follow.
Arguably the most important thing you can do to secure you WoW account is to get one of these. When you log in to your WoW account you are prompted to, along with your username and password, enter a six digit number given to you by your authenticator. This number changes often and can't be reused. Even with your name AND password someone without your authenticator will be unable to log into your account.
The unit is $6.50 and shipping is free. Buy one (click here if you're not in the US). There's also a Mobile Authenticator program available for certain phones.
2. Virus Scanner
Another big one, especially for Windows users. There are a number of programs that will do the job and some cost money but I find the free ones to do fine. A couple of good, well known free virus scanners are AVG Free and Avast. Personally, I use Avast. Nothing is perfect, but either should catch most/all trojans and other unwanted garbage you might run into.
These can help a lot, especially if something nasty makes it into your system and attempts to "call home" from within your computer. There are software firewalls such as ZoneAlarm and Online Armor but me, personally I prefer to use a hardware firewall. If your computer is contected to a Router, you already have one. If not, I'd highly recommend getting one. I personally use one of these and love it.
4. Keep your system up to date
Remember to keep windows and all your software up to date. Check for new versions often and apply them as they release. This will help patch vulnerabilities and fix bugs that may cause trouble. Especially things like windows security updates and virus scanner definitions.
5. Use a better browser
Perhaps a minor point, but if you're using Internet Explorer... STOP! There are far better, faster browsers out there with far more features. Older, more outdated browsers can be security risks, especially Internet Explorer. I use Firefox but there are many other good browsers such as Google Chrome, Opera and others.
6. Don't be a dumbass!
Probably the most important tip of all, use some common sense. If you get an email claiming to be from blizzard wanting you to log in or clink a link, be wary. Never trust messages you might get in game about winning something or beta access or anything like that. Remember that blizzard will NEVER, EVER ask you for your username and/or password.
Also NEVER buy gold or use any "power leveling" services as these are enormous security risks and bad for the game itself. Never share your account information with anyone no matter how much you trust them. A little common sense will go a long way. Some claim that this is really the only really REQUIRED step but I say nothing and no one is perfect. People make mistakes, no matter how smart they are. Follow these steps and you should be able to sleep easier when it comes to your WoW account.
Have I missed anything? Leave a comment and let me know and I'll add it to the post.