Having a good foundation with basic counting and math skills is important for children in kindergarten, so games that require counting objects and groups of objects or just practicing counting to higher numbers is good practice. Children can play board games where you roll multiple dice to figure out how many space you move, to help develop mathematics skills. A good game for counting is "Hide and Seek." "Hide and Seek" involves repetition of counting to higher numbers, like 20, which doesn't often get practiced when counting objects.
Games that involve movement help kindergartners develop muscles as well as balance and coordination. "Duck Duck Goose" is a great active game because children move around a lot, but they also have to practice turn-taking and patience. "Red Light Green Light" is a game that lets children run fast but requires them to practice control by stopping quickly. Any simple game like these that gets children up and moving is good for developing strong muscles and motor skills.
Some games are fun for kids and help them learn to focus their attention better. Games like "I Spy" are rewarding because kids feel accomplished when they find what they're looking for, but they also must look very carefully for something. Other games requiring attention are things like "Follow the Leader," where kids have to pay attention and mimic the person assigned to be the leader, and "Simon Says," which involves doing actions but only under certain circumstances, and helps kids attend to details and lets them move around.
Manual dexterity is something that has to be acquired through practice, so games that involve fine motor skills to accomplish tasks are great for kindergarten children. "Pick Up Sticks" is a game that involves using one stick to lift up another without disturbing the rest of the pile, so it requires a lot of precision. "Operation" is another game where you have to use small, careful movements, which is good for children because it helps them practice control over their hands. You can also make up dexterity games using chopsticks to move objects or spoons to lift balls into containers.