Most of the games I sell is for 10 years old and up, but you should get your young children into board gaming early. Maybe not when they are toddlers, but a little older than that. The reason is not so I can make money off your kids when they reach 10 years old either. That's just an added bonus.
It's a great way for parents to interact with their young children while having fun. You all play together trying to solve the puzzle or get around the board. It helps with their social development when you are laughing and having fun together.
Also it helps with the emotional development. Do not let them win all the time. They need to learn to lose. Then when they lose, they need to learn how to win. Winning shouldn't be an entitlement, but a reward for their problem solving and cognitive skills. Losing a game prepares them for when they fail in the future and how to react to it.
There are many games you can play with your children that are not Monopoly or Candyland. A deck of cards can gives endless possibilities. This is a must to teach your kids. The game first game that comes to mind is Go Fish and the second is War. Simple games. Though play War sparingly as it is more than just a game of chance with not much skill. Go Fish teaches them to find matches and to learn what chance the player has a card they need and to not reveal what they have.
A Rubik's cube is not a board game but it is a puzzle game you can play anywhere. I never was able to solve in when I was young, but there is such a movement of young people solving this puzzle. It will definitely help develop with your kid's problem solving skills.
Cooperative games like Forbidden Island and Forbidden Desert are great games for young kids. Even though they have a minimum 8 years, you can help your younger kids as everyone works together to defeat the game itself whether it is collecting treasure on a sinking island or gathering parts of an airship in the brutal desert environment. Everyone wins together or lose together. You have to think of strategies to defeat the game as you are racing against time and have only a limited amount of actions you can do per turn.
A competitive game that is good for young children is Ice Cool. This is a dexterity game where you have to use physical skills to play. In this game you are flicking a penguin across the board with your finger. Either you can play as the Catcher and try to hit other penguins by flicking your penguin into them or you are trying to flick your penguin as far away to escape from the catcher. Great game to learn motor skills with your hands.
Another game is Karuba where you play a hunter in this puzzle tile game. Each player has their board which is the island and they lay down tiles to connect a path toward the temple. You race against other players. This helps with problem solving skills as well as cognitive skills to learn to rules and apply them.
There are so many games out there for young children to learn. Keep playing board games.