Balloon Popper
This game is fairly simple. All you'll need to run it are some balloons and a sturdy chair. Inflate all of the balloons so that they're full, and then have one person sit in the chair with the balloon in their lap. The remaining people will take turns by plopping themselves into that person's lap and attempting to pop the balloon. If the person doesn't pop it on the first try, then they have to bounce up and down until they've popped it or they give up. This game can lead to some playful hilarity, but supervision should be present to make sure that no one gets injured or out of hand.
Name That Tune
A classic party game can be easily upgraded for a high school party. Name That Tune is a simple game where a snatch of a song is played, and then the listeners have to try and name it. For a high school party, it's best to choose music that's popular with the group, and to get a decently large selection so that it will be something of a challenge and include the likes of a large part of the group. Make sure that the songs are appropriate as well. It's a good idea to separate a large group into teams and keep score, so that you don't have people randomly shouting answers.
Forbidden Letter
A game for the more intellectually demanding, Forbidden Letter is an interesting, tongue-twisting game. The way this game works is that the players all decide on a letter, which is from then on forbidden from conversation. This means that no words that contain that letter (which should generally not be a vowel unless people want to make things very hard indeed) can be spoken. One player is a questioner, and the others answer his questions, but everyone is bound by the rule of the forbidden letter. The last player left standing is considered the alphabet king.