For me, I have played a lot of classic card games, specialized games, and TCGs.
My grandparents like to play a lot of card games and learn new ones from my Uncle Jim and Aunt Laura. They teach us new ones when they visit.
Some of the great ones with classic cards include Agony, Shang Hi, 6-pack, Rummy, Solitaire, and Blackjack.
Of the specialized games, I like to play Skip-bo, Majang, Phase 10, Rook, and Sequence.
My grandparents brought Rummikube with them, but we were not able to play it yet.
TCGs I have played or have a small set of cards include: Pokemon, Digimon, Yugioh, Magic, World of Warcraft, Neopets, Inuyasha, .hack Enemy, Lord of the Rings, Magi Nation, and Bionicle.