Board Game Arena

Memoir '44, azul, carcassone, castles of burgandy are some good ones. If you look at the number of games being played on the tables page (www.boardgamearena.com/gameinprogress) you can see how many turn-based games are being played for each top game and it may give you some insight as well.

my current favs to play turn base due to having time to plan and using the notes feature to plan moves makes it easier to organize:

Ticket to ride, Welcome To, Lost Ruins of Arnak

Isn't the answer to this question simply to eliminate all the games that absolutely cannot be played turn-based (like Spot It), work best with real-time discussion (like Werewolf), or don't have clunky mechanics that require people to react to something you did during your turn before your turn is resolved (and that's not even a deal breaker for some people)? Then whatever remains is just a matter of taste and the question collapses into "what games are good?"

I interpret the question as "which 2-player games don't have clunky mechanics (or very short and very many turns)?", at least those are the ones I'd consider good for turn-based, without considering the quality/appeal of the game itself.