Group Games
Some games are great for a group setting. If you have a free period between classes, and are allowed to borrow an empty classroom, try to get as many kids together to play assassin. Players sit in a circle, and are handed slips of paper, all but one are blank, marked with an X to designate the assassin. The assassin can kill people by winking at them, and the other players have to identify the killer by watching for the wink. For another fun game, charades, act out movie titles while your friends try to guess what it is.
Card and Word Games
If you can fit a small game or a deck of cards into your bag, there are a few great games you could play in school. Bananagrams comes with a small pouch full of letters, and you and your friends try to make the most complex crossword puzzle you can. Slightly larger, Apples to Apples uses cards with words on them, and you and other players make comparisons for one player to judge. With a deck of cards, you could play a game like hearts or rummy, although your teachers may frown on gambling games like poker.
Simulation Games
There are a few games, like Avatar U, which simulate the school experience. In it, you can make virtual students and send them to classes and teach them. Wooz World is a massively multiplayer community where your character can go from a generic player to a superstar of the "Wooz" world, making new friends along the way. These games are located on gaming websites, which may be filtered by your school's network.
Miscellaneous Games
There are other games centered around high school scattered around the Internet, such as A Day at High School, a point-and-click adventure game where you play the game by clicking on objects in an attempt to get your character through the school day. In High School Cheerleader, you must press buttons at a certain time to make your cheerleader dance to the music. There is also High School Makeover, where you can dress up a date to the dance so he looks cool.