Puzzle games (either straight puzzles or with an interesting plot like Syberia), old-school RPG (think Wizardry not Elder Scrolls), logic games, word games, hidden objects, some baseball games (that involve strategy more than hitting home runs). I liked Journey on the PS4, so world-exploring. Sid Meier's Pirates! LA Noire was good for me because it had an overall plot with individual episodes, character, puzzles, shooting, and driving (I terrorized the streets of 1947 LA).

Don't care much about graphics, except I don't like cartoonish graphics. No graphics is also fine--the first game I really enjoyed was Colossal Cave Adventure.

Games based on real-life simulations like the Sims stress me out, and I'm not a fan of point-and-shoot. Also can't get much into world-building games like Civilization.