Apart from the obvious (nobles, monarchs, etc.) I'd say the single most rich entity in Thedas is the Chantry/Divine.
With Andrastian faith being the dominant religion on Thedas, they can reach audiences from all classes and nearly every country, and their policies can practically be felt in every nation (with exceptions being Rivain, Par Vollen and the Wilds). Their mere scope of influence assure them riches.
But then you have to consider the politics and interest of the modern Chantry. One of the major problems expressed in the game, is that the Chantry in the Dragon Age has mostly been focused on consolidating its power. They will take alms, make use of its national connections, and utilize what's left of the Circles to gain wealth and riches, while at the same time only spending that wealth on themselves and not to the needy or the faithful.