If you're referring to web-browser games, I play a lot of the stoff at Kongregate.com. They're partnered with GameStop and always have tons of content. Plus, if you have a PowerUp card from GameStop you can link it to your account and earn points on it for completing a daily game challenge. They have games ranging from shooter to tower defense to mystery, and even a couple MMOs.
If you mean full games connected to the internet, I play Guild Wars 2, Minecraft, Call of Duty, and Borderlands 2. I used to play WoW and a few others, but they all fell to the side as I got bored, leaving me with a core set of games that I enjoy indefinitely.