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.
In addition to the difficulty of playing the class, there is a second element to the mage, one I like to refer to in terms of family. As a mage, people look to you much the way they look to their mothers: they expect you to be there for them, providing them with nourishment and travel services whenever they need them. If you are not the type of person that enjoys stopping in the middle of your Auction House searches to make 4 stacks of water for someone, then maybe a mage isn't the class for you. Where some classes can log in five minutes before a raid and be ready to go, mages have to log in sometimes an hour ahead of time to conjure enough water and food for the raid. Yes, this will definitely change as Ritual of Refreshment is added to the game, but the expectation that you will have to provide 25 people with food and water free of charge is still there.
Despite all of this, there is a lot to love about playing a mage. From your first levels you are able to deal massive amounts of damage. It can go to your head sometimes, this powerful DPS, and leads to the reputation mages sometimes have of being egotistical. Although it is incredibly difficult to play a mage in PvP, once you learn the skills you are a highly coveted player, for both your damage dealing and your crowd control. But when you roll your first mage, I must forbid-yes I used the word forbid-you to delete the character until you level it to ten. It is then that a mage receives Frost Nova, the spell that will make leveling alone actually enjoyable. Mages are excellent for AoE grinding, they are coveted for the crowd control in instances, and they are just plain cool. Who else can transform their opponents into helpless farm animals with the power of their mind?
In the end, if you are thinking of rolling a mage, I say give it a try. But beware: In the words of a certain Disney character, you will get phenomenal cosmic power! But teeny weeny hit points.