One of my favorite things to do with an improv team is to get them to try to play scenes straight. (This refers to "not being a clown" not sexual orientation). Nothing can be more interesting than performance games where funny improvisers try to be serious.
I learned this the hard way in high school. I was the husband in an Agatha Christie play. My wife had just been murdered, and I was supposed to yell, "she's dead!" in anguish. What came out of my mouth was a deadpan, emotionless, "she's dead." My friends, thought my deadpan interpretation was hilarious, and they started laughing hysterically at the most emotional/touching part of the play. That ended my attempts at drama.
But on a lighter note, here are a few games that help explore the humor in playing scenes straight. There are some built in gags, which make these funny, and they have to be set up right by the MC.
1. Scene without expressions. The idea here is to get a really emotionally charged scene from the audience, and then the actors aren't allowed to show any facial expressions. Usually this looks like something between robots trying to act and Asperger's Syndrome. Either way, it's golden.
2. Serious Theater. The idea behind this game is that the actors have to try to play a serious scene without making the audience or any other member of the team laugh. If someone is caught trying to be funny, or makes someone else laugh, they're replaced in the scene with a more serious actor. Usually the tension in the audience or on the team makes laughter erupt. About, the only way for this game to fail is if somebody tries to be a clown because it instantly dissolves any good tension in the room.
Tension can be a wonderful thing in comedy. And, playing it real serious helps.