After I grew increasingly disappointed at the Dominions 3 demo (I know graphics don't make the game, but if you can make 3D graphics for battles that you can only watch anyway, you can make unit graphics you can actually keep apart from each other!) I did a little search for turn-based strategy games and found another one with a fantasy theme: Battle for Wesnoth. I have to say, it's pretty addicting. You control fantasy-themed units on a hex grid and try to take out the enemy's leader (reminds me of chess). If a unit kills enough enemy units in battle, it can "level up" and become a superior version while healing itself fully. Strategy is about positioning your units so that they defend well - i. e. they are on favoured terrain (for instance, elves are hard to hit in forests while dwarves rock in mountains), and since there is a zone of control rule in the game, you can form battle lines so your enemy can't get past to take your villages or kill the weakened units you have retreated. Economy is extremely simple and pretty well tied-in with the focus on battle - the villages, which give you gold and upkeep, also heal units standing on them at the beginning of your turn. The game comes with a plethora of pretty engaging campaigns and a number of balanced maps, plus a random map generator (which is good for training matches against the admittedly weak AI, but will come out horribly imbalanced against a human opponent).
The gameplay is simple yet extremely deep in a strategy sense (apparently also well balanced, in the sense that there is no unit without a counter), in my eyes, and in contrast to Dominions 3 the graphics just plain work. Best of all, the game is free, just like ADOM!
If anyone wants to take a look at it, maybe we can play on the multiplayer server sometime ^^