Back to the original question...
The answer depends on whether you're discussing marine organisms or freshwater organisms. Obviously a captive 13 foot tiger shark could kill you but how many people have those in their 55 gallon aquarium at home?
There are a number of freshwater fishes that are sometimes available for home aquariums that are potentially fatal. Some of them include (not an exhaustive list):
Venomous Freshwater Fish
Heteropneustes fossilis - the Asian Stinging Catfish, is very possibly the most dangerous fish sometimes kept in freshwater aquaria. It is a member of the Family Clariidae (which includes the infamous Walking Catfish) and has been known to cause fatalities with venom delivered via its dorsal fin.
Nothestes robusta - the Bullrout of Australia (Family Tetrarogidae) is not known to cause fatalities but has the potential to do so in sensitive individuals. This species causes severe and debilitating pain through the secretion of venom from twin venom glands associated with spines in the dorsal, ventral and anal fins.
Neovespicula depressifrons - the Freshwater Wasp Fish or Leaf Goblinfish (Family Tetrarogidae) has venom glands associated with some of its fins. Generally this causes a painful but not fatal 'sting'.
Thalassophryne amazonica - the so-called Peruvian Monster Fish (Family Batrachoididae) is one of the freshwater species of 'Toadfishes'. No fatalities have been recorded from this fish but some of its brackish- and salt-water relatives like Thalassophryne maculosa and T. nattereri have caused significant injuries to people who have been 'stung' by them and recovery may take weeks or even months.
Potamotrygon species - the Freshwater Stingrays from South America, have caused fatalities and debilitating injuries. Generally inoffensive, they will defend themselves with a barbed spine (or spines) on their tail. Severe secondary infections are often associated with stingray stings.
Hexanematichthys (or Arias) species - the Shark Catfishes of marine and freshwater origin possess venom glands associated with their fins and can deliver 'stings' that are painful far out of proportion to the severity of the injury itself. I have not read of any fatalities associated with the freshwater species.
Pimelodus species of catfish, sometimes called 'Stinging Catfish', are commonly kept in aquariums. Like many other catfishes they deliver a 'sting' that is painful out of proportion to the severity of the wound, suggesting some sort of venom or mucus secretion.
It is important to note here that secondary infections and tissue destruction following 'stings' by some catfishes have resulted in amputations and very lengthy recovery times.
Electrical Freshwater Fish
Very few of the freshwater fish can be considered 'strongly electrical'. The two most commonly associated with human injuries are the South American Electric "Eel", Electrophorus electricus, (really a knifefish and not a true eel) and the African Electric Catfish (Malapterurus species). Only the Electric "Eel is really potentially dangerous to the aquarist. I can personally attest to the intensity (and pain) associated with a jolt from even a small Malapterurus but it is not life-threatening.
'Toothy' Freshwater Fish
None of the commonly-kept 'toothy' freshwater fish pose much of a danger to the aquarist, though they can cause significant injuries to the careless fishkeeper. Piranhas are certainly capable of removing sizeable chunks of flesh and possibly even a finger and I would not want to take a bite from one of the wolf fishes (Hoplias and Erythrinus), especially one of the larger species or any of the other predatory 'tetras' like the Payara Hydrolycus scomberoides or others of that type. The African Tiger Fish (Hydrocynus species) is another group of 'toothy' tetras that can deliver a damaging bite. In his book Fishes of Lake Tanganyika, Pierre Brichard mentions a record of an 'attack' by a large African Tiger Fish on an angler standing waist deep in water. Brichard mentions that "the calf of his leg was entirely bitten off" by the fish.
Interesting discussion,
-Joe
