I believe it depends on what kind of games you like and whether you want to spend money or not.
I like MMORPGs like World of Warcraft and Ultima Online. My husband used to play City of Heroes before the company decided to cancel it. These games let you interact with other players across the country and that seems to be one of the biggest draws for many.There is a monthly subscription cost to play these games in addition to the initial cost to buy the game.
Games like Torchlight, Team Fortress 2 and Diablo 3 are games you can just buy, install and play without the monthly subscription. Some offer both solo and online multi player modes.
Then there are games that are free to play like Facebook's Farmville, Sim City Social and Zynga's Texas Hold'em. You can play many card games at www.games.com that you would normally not be able to play alone and goyk.com offers a wide variety of games ranging from action to fighting and strategy/rpg.