Or Caesar IV, its sequel, although I haven't played that and have no idea if it's any fun - Caesar 3 was. There's also Pharaoh, that I've played the demo of, which is basically the same but with the Egyptian civilization, and the Zeus and Poseidon games for the Greeks as Camilla mentioned. The fun thing about these games is that they're about more than just fighting like most strategy games are, although in Caesar 3 at least, the financial side of things can get exasperating (hint: trade is absolutely crucial in nearly every scenario, but since some scenarios also require you to put a lot of resources into your military, while in the meantime providing necessary services for your city, it can get rather tricky to do all that with your limited finances). Also in Caesar 3 at least, it tends to be very difficult, though not impossible, to recover from Caesar's disfavour. If you don't get your finances in order fast enough, you drop like a stone in Caesar's regard, and then there's really not very much you can do about it anymore - kicking his legions' ass when they come to depose you is satisfying, and actually gains you some favour, but you can't keep winning. It's quite likely that the later games, including the Egyptian and Greek series, have changed things a bit there, so maybe those things are easier to handle there.

In terms of turn-based strategy like the Lords of Magic you mention, I liked Age of Wonders and its sequel Age of Wonders 2 very much - okay story though not overwhelming, excellent gameplay, looks and sounds quite nice at least for when it was made.
Also Disciples 2 (or 1, I suppose, they're really quite identical other than the story), which has a rather good story, graphics, music and gameplay, but has a few notable downsides - it can take up ridiculous amounts of time, among other reasons because losing your main party tends to mean you can forget about the scenario, no matter how much resources you may have acquired, and so you may find yourself going back to the autosave or saved games rather a lot.

Oh, and for a radically different kind of strategy: the ancient Transport Tycoon and its successor Rollercoaster Tycoon (plus sequels) can be loads of fun without any fighting (though not necessarily without any casualties... Rollercoaster Tycoon can have rather spectacular rollercoaster accidents), just focusing on building railways and transport empires in the former, or on the best possible theme park in the latter.