I read tons of forum posts on the main WoW forum that go back and forth about multi-boxing but most of them end up in a flame war and I don't know what to think. I would like to try it but I don't want to get my accounts banned. So, is it against the WoW terms of service?

I know exactly what you mean about the topics ending up in a flame war and there really is a misconception about multi-boxing. Many people classify it as botting but it really isn't. The definition of botting is pretty much having a computer program play your character for you. Since you have to actively be in control of your character WoW in order to multi-box that makes it not a bot.

Blizzard has stated several times they are ok with multi-boxing because there is someone there behind the account even if it is just one person controlling multiple characters. They also do not care if you own more than 1 account (which makes business sense since that puts more money in their pocket…) as long as you do not use Third Party Programs that automate game play. Source

That brings us to the newer argument that revolves around Keyclone and other software programs that do the same thing. (Keyclone is a software program that sends keystrokes to multiple windows on a single computer.) This program is used to send keystrokes to all the open copies of WoW. This program does not automate game play since you have to hit a key in order for an action to happen on the screen. It doesn't automate game play at all, it just sends the keystroke to the different windows.

To get started in multi-boxing check out the Dual-Boxing.com forums which shares a wealth of information on the topic. It has a very close knit community and you can get all kinds of help there from 2-boxing and up.

On a personal note, I have played around with multi-boxing before (mostly 2-boxing) although not a lot but it can bring a whole new excitement and challenge to the game. It is fun but can really cost a lot of money if you plan to get serious about it.