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
Warfare 1917	Warfare 1944
Battalion Nemesis	Battalion Skirmish	Battalion Ghosts	Battalion Vengeance
Creeper World Evermore	Creeper World User Space	Creeper World 2 Academy