What card games does your 4.5-year-old like to play?

I remember Crazy 8s being popular.
However, also Guess Who? and Chutes and Ladders were well loved as well

Uno is great for little ones. It teaches colors and number recognition. If he can count and recognize the numbers SkipBo is also a good choice. There's always memory. If you don't own a game it's easy to make one with a printer and some clip art.

You could also ask him to make up a game. Cut him some cheap cover stock cards. he gets to do the art work and make up the rules. You can play it with him and help him figure out what rules work and what needs to to be adjusted. it's fantastic logic training. He has to think about how things worked and how they didn't work. Some kids his age can do this and some can't. Usually they will keep the game about their level with rules simple enough for them to adjust and think through. This s something my youngest two have been doing for years. They love to make up games. Some work and some don't, but the process is what counts here. (And it's great entertainment. Kids will spend hours on a project like this.)

My son loves playing Thomas the Train Uno!

My son also loves to play this.. Thomas Match Game

Uno and matching.

solitaire
slap jack

My Pre-K kids love Go Fish, Uno, and War.  You can play War with a regular deck (though our theme decks get used so much they wear out!) and it's great for strengthening number concepts. 



Target often has decks of cards in the dollar section.  Our Star Wars cards came from there and even kids who don't want to have anything to do with "math" will play Star Wars War all morning long.