Are there personality tests out there with questions based on scenarios?
The Kolbe tests have questions like "If I believed something important could be made to help humanity I would:" with a set of 4 responses where you choose one as most likely and one as least likely. These responses might be "Investigate it; Design it; Sell or promote it; Build it"

The purpose of the test is to find your action style and their internal research indicates a high degree of reliability over time.

I will need to do more research to find it, but there is a test used to help pair up college dorm mates that relies just on a series of groups of photos where the individual just chooses one from each group.