I would like here to list possible problems/crisises a space emperor needs to deal with. Some were already listed in above topics, I want here to focus only on various calamities, also if possible, explain these a bit more or provide solutions and try to include especially those that sound fun to you as a player (quality over quantity). Feel free to expand/improve things other people listed as well.
- crushing the rebellion of ungrateful subjects
- a coup of treacherous admirals (more interesting if various admirals lead various fleets and not all of them made a coup)
- poison in emperor's food put there by courtiers (or by some "lover" from the imperial harem that was in fact an assassin). Could be countered by hiring poison testers.
- an alien invasion (interesting if this was just an addition to other internal calamities)
- plague brought by an expedition from a distant part of the galaxy (curfew required? or build more hospitals?)
- smugglers and pirates rampaging through empire (imperial enforcers need to be deployed, if not sufficient an army, but they shot at anyone so it's not the best option)