Spoons: 2+ players
Technically you'll need spoons too. And like musical chairs in the end, you'll use enough spoons minus 1 per kid playing. Sit circled around the spoons while the Dealer (also an active player) sends one card to the left at a time. You're only allowed 4 cards in your hand at once. So, pick a card, drop a card or pick a card, pass it, etc. The object is to match 4-of-a-kind. Grab a spoon when you do! You win; the game is over. The loser, though, is the one who couldn't grab a spoon in time.
Old Maid: 2+ players
Discard 3 of the 4 Queens; the remaining queen is the Old Maid that no one wants on hand at the end. Taking turns fanning-out your cards face down, the player next to you blindly hand picks 1 card out from your hand. The object is to match pairs of the same color and completely empty your hand sans that lone, old queen.
War: 2 players
Split the deck and go head-to-head revealing 1 card at a time; the higher card takes all. If you happen to both reveal the same number/face, yell "war!" followed by presenting 3 more cards face down and 1 card face up. This higher card, again, takes all.
My all time favorite card game was and still is Crazy 8s. Basically you deal 5 cards one at a time, face down, beginning with the player to the left. The balance of the pack is placed face down in the center of the table and forms the stock. The dealer turns up the top card and places it in a separate pile; this card is the “starter.” If an eight is turned, it is buried in the middle of the pack and the next card is turned.
Starting to the dealer’s left, each player must place one card face up on the starter pile. Each card played (other than an eight) must match the card showing on the starter pile, either in suit or in denomination.
Example: If the Q of Clubs is the starter, any club may be played on it or any Queen.
If unable to play, cards are drawn from the top of the stock until a play is possible, or until the stock is exhausted. If unable to play when the stock is exhausted, the player must pass. A player may draw from the stock, even though there may be a playable card in the player’s hand.
All eights are wild! That is, an eight may be played at any time in turn, and the player need only specify a suit for it (but never a number). The next player must play either a card of the specified suit or an eight.
The other game I love is this one. However, like the name suggests it is just for one person. However, it's a great game that works the mind and doesn't involve screentime!
Turn the top card on the 13 pile face up (that's the pile in the middle of the circle). Place the card, still face up, under the pile of that card's number. For example, a four would go under the four pile.
Then turn the top card on that pile face up and place it, still face up, under the appropriate pile. Continue in this manner until the game ends.
If the final face-down card in a pile belongs to that same pile, continue the game by turning the next (moving clockwise) face-down card face up.
You win if all 13 piles become face-up piles of four-of-a-kind. However, you lose if the fourth King is turned face up before all the other sets are completed.