ABCYa.com has 300+ kid-friendly games, some of them quite challenging and fun. The site is free, with banner ads (for things like Froot Loops) or you can pay $7/month to sign in and avoid ads. Unlike some other sites, ABCYa doesn’t seem to use video ads, which we find more intrusive. We tried using ad-blocker with the site, but the games were disabled when we did so. If you have trouble seeing the games, try disabling your ad-blocker.
Most (or all) of the games had been made with Flash, which is supported less and less each month. (Chrome will soon drop support for the Flash plugin altogether, but you should still be able to use Flash games with with Firefox, Opera, or Edge.) But ABCYa has been porting its games to HTML5, which is supported well by all browsers and you should be able to access the games with any device.
Our 4-year-old asks for this site all the time, a few ties each week. There are so many games that they can find something new every time. While some of the games are pure fun, none are violent and most reinforce some educational concept such as addition, letter shapes, etc. We occasionally let the kids use sites such as HTML5games.com but that has more intrusive ads. We prefer that the kids play the games on PBS Kids but many of those games are a bit too difficult for the younger kids.