There are literally thousands of tropical marine fish species kept today. The possible combinations are virtually infinite and depend as much on the individual species as the type of aquarium: FO (Fish Only), FOWLR (Fish Only With Live Rocks), or ordinary with live corals, sessile invertebrates. Except for very large species, almost all species you can see in a public aquarium can also be found in the private aquarium trade. LiveAquaria has a
compatibility chart that is a good
very general guideline, but it should not be considered definite and there are plenty of cases that don't really fit into the chart. Part of this is related to resources and/or size of tank. Public aquariums typically have resources far beyond those of a normal aquarist and huge tanks; in such cases species that generally are incompatible may coexist in peace.
lionfish, puffer, scorpionfish, stonefish, triggerfish
Puffer+trigger are infamous for being aggressive towards lionfish and they are fully capable of avoiding the venomous spines. Especially triggers often end up killing lionfish if mixed (this mix is so problematic that one of the largest marine aquarium forums on the net for years had a sticky thread warning about it). Puffer+trigger are also infamous for having a go at species like stonefish, scorpionfish, and any other slow moving fish. They may not kill it, but it'll get wounds that easily get infected. Except in huge tanks, there are few cases where these combination have worked long-term. However, it's important to mention that especially triggerfish vary a lot in temperament depending on the exact species: e.g.
Xanthichthys are pretty relaxed and often work even with smaller species, but e.g. clown and orange-lined triggers can be pure devils.
Stonefish and scorpionfish are also tricky and there are quite a few cases where they have managed to eat lionfish that only were a bit smaller. Plenty of aquariums continue with this combination, but it is only really sensible if the sizes are closely matched (or the lion's are a bit larger) and even then there's a bit of a risk. It is also worth mentioning that the extremely venomous stonefish are illegal for private aquarists to have keep in some countries.
Moorish idol, mentioned in an earlier post, absolutely should only ever be kept in big tanks (wikipedia quotes 100 gallons but that's nonsense) and only by
highly experienced keepers. Sadly they are still sold in ordinary aquarium shops to people that don't know any better. 99% of those sold to private aquarists end up dying slowly from starvation. It's comparable to most other species that are highly specialized feeders; obligate corallivore butterflyfish, most nudibranch species, etc.
