Do you remember concentration or memory that we used to play with a pack of cards as kids? There's a mahjong game you can get as software which is similar. I've played it as Shanghai, but I found a version on the internet from miniclip.com that is called Mahjong. Although it uses Mahjong tiles, it really isn't the game of Mahjong as we generally know it, but a type of solitaire.
I think it's a great game for when you want something you and your kids can play together online that is not some mindless shoot-em, blast-em. It helps develop their visual discrimination and spatial skills, and truly does require concentration. Yet it can be played by kids (and chooks!) of all ages.
The tiles are digitally laid out in a pattern, face-up, with some tiles having tiles on top while others don't. The idea is to match two tiles by clicking on them. But you can only click on tiles that are free. Free means a tile is not surrounded on both sides by other tiles, or hidden.
There is an ad playing on the site, but I didn't find it distracting. There is also a timer that keeps track of how long you take to release every tile, but there is no pressure, and the background music is pleasant.
If your kids are too young for abstract Mahjong tiles, (Book Chook tip: I make up my own names for them and call them things aloud like the four of bones and the eight of winds to help me remember when scanning the tiles for matches) Kaboose has a simpler memory game they might like, where they match the equipment to the professionals who use it. Or there's a nice Cat in the Hat one at Seussville.