Another card game that's great for adults and older children is Go! Go! Go! But the rules are very complex, so it isn't best for young ones. This game was a feature of the old NeoPets virtual community that was popular when I was a teen. That's where I learned it.
Everyone starts off with nine cards. Three cards are laid face-down in front of the player immediately without being looked at. These are your face-down cards. Three cards are laid face-up in front of the player so everyone can see them. These are your face-up cards. The other three go into your hand, so only you can see them. The rest of the cards are put in a stack.
A card is pulled from the stack and played. Play goes clockwise. Each player tries to play a higher card than the card that was previously played. Aces are high, twos are wild. If a three is played, the next card played must be an odd number (including Jack and King; a two cannot be played on a three). If a four is played, the next card played must be even (including Queen). A player may play more than one card at a time from their hand as long as they have the same face value (e.g. two sevens). Initially, each player will pick up a card from the stack to replace each card played.
If a player is unable to play, he or she must pick up all of the cards that have been played so far, and add it to his or her hand. Play then continues. If a player plays a 10, the 10 and all cards on the played pile are cleared away out of play, and that player gets to go again. The same thing happens if a player plays all four of the same card, or completes a set of four with the player just previous (e.g. Player 1 plays one three, Player 2 plays three threes).
Once the stack is empty of new cards, players continue to play from their hands until they run out. Again, the same rules apply - if you can't play, you must pick up the pile and add it to your hand. Once a player's hand is empty, he or she plays from the face-ups. Only one face-up can be played at a time. If a player can't play, his/her lowest face-up is added to the pile and the player must pick up the pile, which then becomes his/her hand. Once again, the player must play from his/her hand until it is empty.
Once the hand and face-ups are exhausted, a player plays from his/her face-down cards. These are played blind - the player simply picks up a card and tries to play it. If the play is illegal, the player picks up the card and the pile and this becomes the player's hand. Once again, the player must play from the hand until it is empty, then the player can return to playing from the face-down cards.
The winner is the first player to get rid of all of his/her cards.