Kongregate.com, AddictingGames.com and Miniclip.com have online games that are available immediately. All three of these sites have a huge library of games to choose from, with many different types of games to play.
You can view the most popular games if you are unsure of what to play. You also have the ability to view top games in a particular category. If you are interested in achievements and acquiring badges to show off your skill level, then Kongregate is the best site to use as it has an achievement system for registered users.