There are tons of games online, presented in lots of different ways. Some, you can play directly in your web browser. Some are games you can download and play any time. Some are connected to huge online worlds.
Massively Multiplayer Online Games
Some online games put you in a vast fantasy or science fiction world, which you can explore and enjoy at your leisure. Thousands or millions of other players are all in the same world at the same time, too, so you can interact with them, and go on quests together. These games are called Massively Multiplayer Online games, or MMOs.
The most popular MMO in the States is World of Warcraft, which has millions of players. In World of Warcraft, you create a character from one of eight races (human, gnome, elf, etc.) and explore the huge fantasy world of Azeroth.
Online Card and Board Games
You don't need to run around a huge fantasy world to play games online. Lots of sites provide web-based card games and board games, from Hearts to Backgammon.
With most of these sites, you create an account, then join a chatroom and create a new game or join an existing one. Many sites are free, but the more serioues ones require a small monthly fee (usually about $5 a month).
Downloadable Games
There are also many sites providing full-fledged downloadable games, that you put on your computer and play there. These games range from free puzzle games to complex shooters.
Flash Games
While downloadable games are put on your computer before you play them, Flash games can be played directly on a web browser. Most online card and board games are actually flash games, but there are also original puzzle, action, adventure, and many other types of games that you can play this way.
Game News and Reviews
With all these games out there, how do you find them, and how do you know if they're good? You can use game news and reviews sites, which link to trailers, walkthroughs, and reviews of many games.