I played a Shaman for over a year. They are definetly a fun class, and not as overpowered as many people say.
As a Shaman, you have decent melee, but you are also VERY dependant on Windfury, which has an 80% chance of not doing anything.
You also have shocks, which can be quite potent. The problem with shocks is that they all share the cooldown, so you have to decide which shock to use in any given situation. They are also mana hogs, which makes the shaman very mana inefficient.
Totems are great too, and add a lot of flavor to the class, specially when grouping. Warriors will love you if you give them Windfury and Strength of the Earth; Rogues and Hunters will love you with Grace of the Air. Casters will appreciate Mana spring and mana tide. A shaman is a good addition to any group.
Lastly, if you don't like healing, don't choose a shaman, because that will be your role end-game. In Molten Core and beyond, a shaman's role is heal-botting and support via totems.
Mages are very powerful, but fragile. THey require a high amount of skill in PvP since they have such survivability, specially now that they nerfed the trinket combo that let them 2 shot people in PvP. They are reciving a rehaul in 1.11 so it will be interesting to see what happens with them then.
Mages also have the advantage of being a 'pure' class, and hence you can focus only in their primary role: damage, and get as much intellect and +damage items you can.
Shaman on the other hand are hybrids, and have itemization problems. You need strenght, stamina, agility and intellect if you want to be versatile, and will often have to carry several sets of gear to adapt to each situation, which can be a pain.
Oh, and like Schadenfroh said, if you hate rogues, don't roll a mage. SHaman generally have a relatively easy time against rogues.
If you want to run over warriors, though, a good mage should cream a warrior regardless of spec almost always. A shaman (specially enhancement) has almost no chance against a well geared MS warrior.