Keep all of your software up to date
Browser, operating system, any other programs you use should all be the latest version because manufacturers are constantly filling security holes. No operating system or browser is safe, though some are safer than others. If you are on a PC, don't depend on Windows Update alone to keep you current, make sure that all of your non-windows software is recent, particularly if there is no auto-update function. Keep a set of bookmarks for sites to check for new versions and check them periodically. What I use: Firefox 3.x on a Windows XP PC.
Scan with an antivirus/antispyware program daily
It's not good enough to just have antivirus software running in the background. Many trojans can sneak by your regular detection but will be picked up in a scan. A lot of software will require you to change the settings to remove or quarantine the offending program, so even just scanning isn't enough. Make sure that the malware isn't just detected -- it must be deactivated. If the budget is tight, you don't have to worry about actually buying an excellent antivirus program. There are many free options available. Get one and set it up to scan when you're not using it. What I use: Clamwin Free Antivirus.
Don't buy gold or use powerleveling services
I can't stress this enough. I know that some of you rationalize doing this with the idea that you work hard and make good money and therefore don't have time to "catch up" to everyone, so you feel justified in using these services. But there is a whole lot of game on the way to max level that is fun -- it's not just about racing to the end. And these days, getting gold and leveling up is cake. But most importantly, you are putting yourself at risk when you give these people any of your information. It also keeps them in business, making account hacking profitable and more likely. Just don't do it.
Don't fall for phishing schemes
Phishing scares me because of how they prey on everyone from the naive and unsavvy to the competent but careless. The clever ones use logos from the actual sites and websites that are so close to the real ones that they can fool people who aren't really paying attention. Of course, phishing isn't just for WoW accounts -- no online account is safe, even banks. Just remember that no company is going to send you an email asking for every little detail of your life, particularly your account password. Carefully pay attention to where you are clicking and be suspicious of all unexpected emails asking for your personal information. Also, bookmark your favorite WoW addon and info sites rather than typing the names into your address or search bars. These crooks make websites that are just one letter off of the ones you are looking for and ask for info or load you up with keyloggers if you happen into their lair. If you find yourself in one of these places, immediately run a virus scan and don't login anywhere until your system is clean.
Get an Authenticator
There have been no confirmed account hackings if there is an Authenticator on the account., according to Blizzard. Even if that one store is true, one case out of so many sold is really good odds. If you live in the U.S., they are dirt cheap ($6.50) and are shipped for free. They are available in other countries, but the shipping is a bit steep. Still, it is an excellent investment if you plan to play regularly for a while. I just got one and it adds an extra step which is only a slight inconvenience. Also, if you play at internet cafes or on multiple machines, you can feel safer knowing that the extra step will keep you safe no matter how unsafe the system you are using.
Reports of accounts being hacked are on the rise. And don't think that only the hardcore raiders with the leet gear are the ones who have to worry. If these criminals get your info, even if you are a noob with a bunch of low level alts, they will scrape the copper from your pockets and use your characters for their own nefarious purposes. So take these simple precautions and next column, we'll talk about how to choose your addons.
For more information on account security, please read WoW Rookie: Account Security Basics and Account security mythbusting.