What are some good games to play with kindergarteners and 4 and 5 year olds?

Duck Duck Goose, Tag, Red Light/Green Light, Charades (maybe, just keep subjects very basic, like animals or vehicles), Sharks and Minnows, and if all else fails, you can make up your own games.

I Spy

All of the classics Candyland, Hi Ho Cherry O, Go Fish with picture cards. My kids like to play impressions......give me your impression of a fish, snake,ect. we go one at a time and they each get to be the center of attention for two turns each. Play-Doh is also a lot of fun.

Nap Time! Hide and Seek! Tag! the Limbo!

Space bucket! Put a bucket in the middle of the floor and swear up and down it came from space. If the children claim to have seen it before, tell them they've probably offended the aliens now and will bring doom to our planet. Thank them sarcastically.