My son is almost 5 and my daughter just turned 3, for what it’s worth regarding these recommendations.
Haba’s First Orchard was the first game I got my son. It is co-op and mindnumbingly basic, but it was a great way to teach taking turns and following he rules. These days he will take it off the shelf and run a game for his sister, which is awesome. As mentioned, Monza, Animal Upon Animal, and Rhino Hero are all great.
Our current game is My First Stone Age, which I can’t recommend enough because it has taught a 4-year-old how to play a worker placement game. There is a memory element, too, which can be gamed, so any adults would have to throw the game if they want to give the little ones a chance.
Castles of Caladale will be opened in a week. I think most tile-laying games can be good for kids who can at least match the edges. Carcassonne can be simplified for kids.
And my boy loves X-Wing. Throwing all he rules out the window, all kids can select their movement and roll dice to attack things around them.
As for digital games, I really don’t like when my boy plays video games, but somehow I let him anyways. He loves the LEGO games and has actually beat Jurassic World in its entirety, which actually surprised me. There are enough puzzles in the game that I kind of give him a pass with the LEGO series.
The games in his tablet rotate, and when we have a long trip I tend to put more video-game-like games on it to keep him from driving people insane. Aside from the learning games, he likes Hidden Folk, Inks, Cut The Rope, and Thinkrolls.
Finally, there are some really cool sandbox games in iOS for kids to build a little city of some sort. Pango makes a roller coaster park builder and the Dr. Panda series has a game called Hoopa City. He’s probably spent the most time with these. I can’t wait until he can read and reason enough to play a real tycoon game.