Yes, there are lots of games. First is neopets.
Neopets- A fun yet cute game site where you adventure around neopets world, finding games to earn neopoins. No download, you can buy a neopet and get lots more.
Marapets- Is a game, almost just like neopets. No pay or download, but watch out, your animal can die so I suggest kids older then 8 should be playing.
Kooland- You must pay to be a member, but you can play as a guest for 10 days without as much access to the game. It's kind of like webkinz but you get a bigger room, you can't talk if your only a guest, and you can't pick your animal if your only a guest.
Mileyworld- you can play around miley world- I've played and I don't think any pets are involved. No virious's you must pay.. But its fun and you get to win concet tickets, talk to miley cyrus, and if you buy her new CD breakout you can win a free guest pass... To miley world!
Hope this helps, and I heard og gopets its pretty fun and free!