Other turn based strategy games?

Risk doesn't have tiles.

If you like Catan though join my Catan group!

If it's abstracts that you are looking for this site has 19 games (no, chess is not one of them ):

http://vying.org/

My favorites: Amazons, Ataxx, Cephalopod, Connect6, Hexxagon, Nine Men's Morris and Keryo-Pente.

Very old topic, but the game Legions at war looks like the chess game for the future. Still in development it captures the elements which made chess great but puts it in a modern setting. It also offers you the ability to play chess on different boards sizes and unit setups. 

Tic-Tac-Toe

If you like board games, you should be on this website: https://en.boardgamearena.com/ 

Over 100 free board games that you can play turn based or real time. It's pretty cool.