I've never been into crossword puzzles, but I really enjoy the game outwitters:
http://onemanleft.com/games/outwitters/Despite the graphics on that page its a relatively simple yet complex turn based game. Some people compare it to chess. You have units with their own offensive and movement rules and you try to attack your opponents base.
Its turn based and a very quick game might take 8-15 turns, my longest game was about 260 turns. Its a "free" game but quickly you will want to by extra turns for a few dollars since sometimes you need to wait a day for the other player to make their move. Generally I have about 15 games going so some turns area ready throughout the day. Sometimes you get a player that makes turns real time with you but others might be in another time zone so there is a good gap between turns.