It is certainly possible to beat Dragon Age with any class, but I'd say that mages are the most powerful. The main reason is that they have just superior crowd control abilities, you can freeze the enemies, paralyze them, put them to sleep, put them in a force field and so on. And you can deal some serious area of effect damage as well.
I'm a big fan of a two mage party, but you have to actively manage your mages, setting up the AI for that is not really easy.
I have to say that I played mostly when the game was new, I haven't played much after the patches came out. The advantages of the mage have been reduced somewhat, but they are still very powerful.