I have a group of friends that enjoy trying out new characters. Sometimes they ask me this very question, and I reply with some questions in return. First is the easy one: where do you prefer to be in a fight? Do you want to stand up close and personal, breathing in the putrid stench that is the monster's breath, hacking away at him piece by piece? If so, then a mage isn't for you. They are a cloth-wearing DPS class, and with the exception of a few fights, we are standing at the back of the crowd dealing death from a safe distance.
Also, I like to ask: How difficult a challenge are you looking for? Mages are not the easiest class to play. They take a lot of juggling. With the various spell resistances of the monsters in Azeroth and Outland, a mage has to keep constantly aware of who they are fighting. Your spell rotation can be totally different depending on who or what you are up against. I've heard it said that anyone can play a mage, but few play them well.