Depending on the kind of targetry I would say a plate race or something of the sort using paper targets is the most common. There could be accuracy shooting like Irving said. Whatever you do you could throw in shoot/no-shoot targets, reloads, dummy rounds, barricades, etc. etc.

I always thought math games are fun. Say you have up 20 or so IPSC targets or section targets off to save on targetry, then number each section from 1-20. Give the shooter a math problem and have them shoot the target with the corresponding answer. That mixes up a lot of different/important principles for people and really screws with their head (especially when being timed) but it's fun. Some people may not be to interested depending on math ability. I know I hated it at first but they grew on me and my target acquisition, scanning, and ability to kill dots quicker really improved.

Taking a simple plate race and throwing in crazy positions or drills (VTAC drills for example like the Tri Lamda, 1-5, Highsmith, etc.) can make competitions fun as well but maybe that's for the more experienced shooter.

As a big drag racer and shooter, a crazy course with a heads up bracket like Irving suggested sounds awesome as well.

I'd love to shoot whatever you guys want to do.