I like playing single player intellectual games such as puzzles, crosswords and sudoku. As for two player games, I like checkers. Even video games require you to concentrate and use your brain to come up with solutions so I sometimes like playing challenging video games such as Uncharted, Call of duty, etc.
My favorite intellectual game is without a second thought poker. I just love the strategy of when to bet versus when not to, when to call and so on. It's not about only mathematics, but also about strategy. The thrill of having real money involved takes you strategical thinking to another level. It's a game for clear minded people. If you let your emotions overwhelm you you won't last long.
I also like games that test your brain and intellect. I used to play a lot of Chess too, but now my favorite would be Scrabble. I enjoy it a lot, also I feel one can learn a lot (improves vocabulary) from it as well. Crossword is another one that I enjoy.
Scrabble is my absolute favorite because it's the best way to expand your English vocabulary... And it's fun. Really fun
When I'm alone I enjoy playing Logic-Grid puzzles, they're a really fun way to put your logical thinking in practice. Resolving it at last gives you this huge sense of satisfaction... When I'm free (which is almost never when you're a student!) I can spend hours solving these without even noticing.