Most of the games use Adobe's Flash player. Get the latest one at http://get.adobe.com/flashplayer/. A few other games use Adobe's Shockwave player. Download it from http://www.adobe.com/shockwave/download/.
Because of the large number of Flash games, they have been divided into different categories:
If that doesn't help, You can write to Squigly and he will try to help you.