There are enough great games.
Already mentioned Lords of Xulima, Shadowrun series, Xenonauts and Battle Worlds Kronos.

Also you could try Halfway or Bionic Dues.
The Last Federation is turn based too, but turns run simultaneously (like real time with pause in intervals). Check a gameplay video if you'd like.

Unfortunately Wasteland 2 Director's Cut has performance issues (it's unplayable), while the original version runs smoothly on my system.

Lords of Xulima
Wasteland 2
Shadowrun (all of them)
Pier Solar and the Great Architects


I'm currently playing through Lords of Xulima with over 24hrs in it already, this game came quite a surprise to me. It has very good storytelling, a huge map to explore and challenging gameplay.

Most things have been covered, I approve. Of the rest, Jagged Alliance 2 can be run natively, there's a cross-platform engine reimplementation (Stracciatella). Or how about some Tales of Maj'Eyal? It's a roguelike, and it's actually Free software, so you can try it out before buying it (or donating directly to the developer (or buying the expansion)).

I was going to suggest you try the demo of Telepath Tactics as well, but apparently GOG doesn't carry the Linux version. Which might be for the best, considering it's a Flash (AIR) game. On the other hand, said demo worked fine for me, on the same computer the dev's previous game (Telepath RPG) was nigh unplayable.

Just did. The game runs too slow. It's still unplayable. :-(
Removed for one more time from my system. :-(

I tried the minimum settings. The original version runs smoothly at almost full settings (all full, but SSAO and anti-aliasing off at 1680x945).

Nevertheless Director's Cut version runs almost like the original on Windows 7 64-bit (with -force-d3d9 parameter) on the same system.

I don't know why this happens, maybe it has something to do with Nvidia Linux drivers and not with the game itself.

Anyway I can play on Windows, although I prefer Linux.

My system is based on Intel i7-620M, 8 GB RAM, Geforce GT330M with 1 GB dedicated VRAM, 2x500GB HDDs (Mint 17.2 64-bit on the first disk and Windows 7 64-bit on the second).

This is the winner so far. I am enjoying it a great deal so far.