With a deck of cards.....Snap, Go Fish, Crazy 8's (I know at least 3 variants), poker (again there are variants), Bridge, Whist, Canasta, Euchre, Patience/Solitaire (again with variants)
Common dice-and-boards.....Trivial Pursuit, Taboo, Monopoly, Snakes & Ladders, Backgammon
Other popular games.....HopScotch, "Chinese" Jump Rope, Red Rover, Statues (Red Light), Mother, May I?, Boggle, Chess, Checkers (Draughts), Chinese Checkers, Noughts & Crosses (TicTacToe), Hide & Go Seek, Marbles (Alleys), Battleship, Connect 4, Parcheesi, Scattergories, Pictionary, Scrabble, Twister, Candyland, Charades, Hot Potato, Musical Chairs, 20 Questions (Animal/Vegetable/Mineral), Hot/Cold (Hunt the Thimble), The Farmer in the Dell, Pass the Parcel, Pin the Tail on the Donkey, Blind Man's Bluff
Extraneous.....all the counting-out rhymes to choose someone as "IT" (Eeny Meeny, Engine Engine Number Nine, etc), Rock-Paper-Scissors.