I like games which require the use of strategy to win. Here are some free strategy games from various sources which you can play online. Some Logic Puzzles are also available.

gemcraft gemcraft-chapter-0 GemCraft Labyrinth
Gemcraft Gemcraft Chapter 0 GemCraft Labyrinth
warfare-1917 warfare-1944
Warfare 1917 Warfare 1944
Battallion Nemesis Battalion Skirmish Battalion Ghosts Battalion Vengeance
Battalion Nemesis Battalion Skirmish Battalion Ghosts Battalion Vengeance
Creeper World Evermore Creeper World User Space academy 
 Creeper World
Evermore
Creeper World
User Space
Creeper World 2
Academy