Two amusing examples from distributed computing are:
The Bysentian generals problem. The problem asks for an algorithm that allows a large number of processors to reach a consensus on something (say a bit value) when some of the processors behave in a malicious way. The original paper motivated the problem with a fictional story of account of Byzantine generals trying to coordinate a joint attack. There's also a related "Chinese Generals Problem".
Paxos algorithms. This is a family of algorithms that also allow a number of participants to reach a consensus. These were introduced by Leslie Lamport in paper written as a story about the downfall of an ancient Parliament on the (fictional) island of Paxos. The story ends when the parliament inadvertently restricts membership to dead sailors which, of course, can then not be corrected. As you can read about here, the novel exposition of the paper led to a very delayed publication of what has since been recognized as an important result (and is reportedly used in Google, Microsoft and IBM products).