I'm not sure how much "strategy" they have to be. Two of the games I list ain't exactly "turn based strategy" like your usual 4X. Still, they're turn based and mostly about careful gameplay so I think they are worth listing.
In case you don't wanna read through this hold post I will first post a list of the games. It's ordered by how good I think games are (means by how much I want others to try them) with top being the best:
Darkwind, car combat
Space Rangers 2, spaceship rpg
Sid Meier's Alpha Centauri, best of all civs
Dominions 3 //
Heroes of Might and Magic IV (can't decide which is better)
Darkwind is a turn based car combat game and might not be what you consider a "turn based strategy game", fair warning. It features a persistent world, means your drivers get skills, die (often!), you get money and all that stuff. It's basically free to play, but you don't get to design custom vehicles and miss out on some of the advanced stuff. "Advanced" stuff is not why you should play this, though, so the pay-to-play stuff really isn't needed.
The reason you wanna play this is the awesome events you will see. The "turn based" part means players have some time to set up great and accurate moves, that makes it very strategic and tactical. It's pretty complex, with text messages when your driver gets their nose rammed through their brain and all that funny stuff, similar to DF. Basically a very advanced version of the cool/epic/funny things you will see in ZK when people micro their units very well. A group of cars ramming into each other, doing back flips, exploding and what not. Under constant development. (
Trailer from 2009, not very up to date)
Space Rangers 2 (and maybe 1, though I didn't play that) and might not be what you consider a "turn based strategy game either". It's a turn based game where you fly around a galaxy, do the usual things like mine asteroids or trade or hunt down pirates or be a pirate yourself. The fact that you can hire some other ships and eventually command military makes it a tad strategic.
There's many missions to be fulfilled, all of which vary greatly: tycoonish missions, text adventures, simple kill x within a given time, deliver y to planet z, etc.; The game features an arcade like minigame, as well as a mini-RTS. All of this is wrapped up in a simple story and lots of jokes in the form of funny references.
Licho already suggested
SMAC. I think it's the best of any civ game. I played Civ, Civ2, Civ5, Freeciv, Freecol, CivNet and games with civ in their name that only have little in common with Civilisation (eg. Galciv). SMAC wins.
Dominions 3 is a rather complex turn based strategy game with lots and lots of content. There's just so many units, spells and whatnot. It's more epic-scaled (with a map similar Risk, although I never played that :P). Battles happen at the end of every turn without players giving commands. Players merely set up formations and the like.
Heroes of Might and Magic IV (everyone says 3 is the best, but I only ever played 4) is a turn based RPG (as in some of your units are "heroes") and strategy game. It's got pretty simple gameplay with various factions, resources and units. The really nice things are beautiful 2d terrain and very very nice story driven campaigns. There's just so so much to explore. To be honest I don't really like the actual gameplay, but I keep coming back to it for the story element. Played it every now and then for a few years now and still didn't even complete a quarter of it.