Many of the issues that you will find with World of Warcraft security are the same ones that remain relevant in overall computer information security.
Since your World of Warcraft account is dependent on a password system, it is important to protect yourself from key logging, which is when a program records your keystrokes. This can come from computer trojans that give people remote access to certain parts of your computer.
The best way to protect yourself against this kind of possible breach of your World of Warcraft account is to increase the security level on your computer in general. This means including a firewall that will prevent remote access by World of Warcraft account thieves.
Trojans, which come in the form of .exe files, will often be offered as some type of World of Warcraft cheat. Make sure to avoid these as no .exe file will be a legitimate World of Warcraft cheat. To combat trojans even further you can use a combination of different software that can detect and destroy these infiltrators. Spybot Search and Destroy has conventionally been used to look for "spyware" as it relates to pop-up advertising, but Spybot will also scan your system thoroughly looking for software that could be dangerous.

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SUPERantispyware is a similar shareware application that works like Spybot Search and Destroy, except it is consistently updated to respond to new adware, viruses, and trojans. Lavasoft's Ad-Aware is also a good scanning application, though it is not usually going to be as efficient as either Spybot Search and Destroy or SUPERantispyware.
All three together will give you the computer protection you need to fight off any attempts at key logging.