Texas Holdem - I like to both play and watch, watching any videos (High Stakes Poker, for example) that I could feast my eyes upon, as well as the tournaments. This also feeds nicely into my interest in psychology.
Online Video Poker. Free, not for money.
Hanafuda (Koi Koi) - A seriously fun card game. I first learnt of its existence in a game called Yakuza, and went and ordered me a real set of these cards. You can aslo play this online for free.
3 and 4 - This probably has an official name. To discribe this game simply, you're just taking turns picking off piles until someone gets 3 of something and 4 of something, 3 Qs and 4 2s, for example. Fun card game.
Solitaire, on my PC - I find this very addictive. It became a ritual of sorts to play this before bed every night at one point, and I'd make up stupid rules such as having to win a game before I could sleep. I've recovered and can just play this casually now without all that stuff.
Scabby Queen - Usually the queen of hearts. All cards are dealt out and each person discards all their pairs, leaving them with lone cards in which to play with. Your job is to avoid picking and being left holding the scabby queen.
I've played and enjoyed Gin Rummy, Blackjack and even Hearts, although I found Hearts somewhat confusing. I've played other card games but unsure of their names.