The Great War of Prefectures plays like a cross between Risk and an RTS, with Japan's prefectures (analogous to other countries' states or provinces) serving as the territories you fight over. Despites some interface flaws, this game has that elusive quality that will bring you back for more even after you thought you'd had enough.

Tantrix is a friendly one-player version of the 1988 board game by Mike McManaway, a game that may not have the renown of Scrabble or chess, but still attracts devoted players for annual tournaments. Try to form loops of a single color out of specially-designed hexagonal tiles, in either a puzzle mode or the more improvisational Solitaire mode.

These puzzles are the same type of chess mind-benders that still appear in some newspapers next to the word jumble and bridge game brainteasers. Given an endgame position consisting of a few pieces, try to produce checkmate in a given number of moves. The difficulty curve eases you in gradually, and if you're good enough, you can tackle 650 unique puzzles. Regardless of your Elo rating, you'll find a challenge that will suit you with MateMaster.