For me, typically the longer the game, the more addictive it is.
Think Sokoban or Chip's Challenge but you have to rewrite the rules of the game to solve puzzles.
Going away and coming back later probably helps solve a lot of the puzzles.
The premise is simple: Dive into the dungeon, retrieve the famed Orb Of Zot, and abscond with it in your possession. Easy, yes?
What sold me were the vi-style controls, the ability to play directly from a terminal (or a prettier web GUI if you so choose), and how every action is on a turn-by-turn basis. You get to pause/stop at any time, and your progress remains for years.
It can be a little daunting to get into it, but it is a lot of fun!
Tsumego Pro is a nice app for quick, short-term life and death problems with a range of difficulty.
If you are new to go, check out http://playgo.to/iwtg/en/ -- it's a solid introduction to the game.
Codenames online play with friends, no signup required .