The "Easy ASP" [0] tutorial from Potassco can walk you through some examples, if you'd like.
The playlist is aimed at a general scientific/business audience, the presenter suggests that a lot of natural and business systems can be described in this manner. The presenter also mentions how a Clingo program was used, without modification, to optimize radio frequency band allocation.
Here's a repository [1] of ASP programs in clingo. Under problem classes, I see mostly: game AIs, graph problems, various puzzles, so on.
