Most saltwater fish are too difficult for the average aquarist to breed. However, certain species have bred in captivity. Rearing the young is extremely painstaking in some, and impossible at the moment in others.
For instance, Pygmy Angels (
Centropyge spp.) have been bred in captivity, but the larvae are extremely difficult to care for. People also pass up captive bred specimens because the coloration is not as bright as those that are wild caught. Case in point for wild caught over captive bred would be the Flame Angels (
Centropyge loriculus), the cb specimens tend to be more orange than the highly desirable deep reds of the wild caught ones. Even worse are the Lemon Angels (
Centropyge flavissimus, cb's are a faint yellow, wild caughts are bright yellow.
Certain Clownfish and Pseudochromis have been bred in farms many times. Prices are much higher than the wild caught ones, which is part of the reason why wild caught specimens still make their way into the hobby.
While the Flasher Wrasses (
Paracheilinus spp.) and the Fairy Wrasses (
Cirrhilabrus spp.) have been bred in captivity in large public aquariums, rearing the larvae has not been achieved. If I'm not mistaken, someone also told me that it wasn't feasible for some reason or another, idk.
Tangs/Surgeonfish have laid eggs in captivity, but the larvae stay in the larval stage for a very long time, until something triggers them to get out of that phase.
What I'm about to say is debatable amongst the saltwater hobby, but I will mention it based on my experiences.
Many reef fishes are usually kept in solitude. I've found this to be very problematic for certain fish. They tend not to exhibit the same set of behaviors as when they are kept in groups. Not to mention, they also tend to be less boisterous and active. From what I've seen, some species look lost and become very shy when they're kept in solitude compared to when they are put in with other fish of the same species in much the same way as their natural social structure would be. Unfortunately, the price of each fish deters many people from purchasing more than one of each species of fish so some people can't see the difference. Even worse, some species of fish absolutely must be kept in groups or they will slowly decline and die within a relatively short period of time.
The biggest problem with keeping saltwater fish in groups is that many species command large territories, so a tank that is smaller than 100 gal is totally out of the question.
Reef tanks are highly sustainable, but very difficult to maintain over a long period of time. Certain corals have been known to spawn in captivity. Coral spawning is complicated, but most of the ones that breed in captivity the easiest incubate their eggs inside each polyp and cast out the planula larvae once they hatch. Although it is extremely rare, some corals have done what is called a mass spawning in captivity. Fragging small polyped stony corals has been going on for roughly 15 to 20 yrs already. Some species of large polyped stony corals can be fragged too. Most species of soft corals are ridiculously easy to frag.
Giant Clams (
Tridacna spp.) have been farmed for years.
There are of course still species of fish, corals, and miscellaneous invertebrates that an aquarist should never purchase because of their specialized requirements, but they still make it in the hobby because they sell. Sometimes these species are sold to an unsuspecting aquarist (aka the person selling the animal is outright lying or telling half-truths to their customers about the animal in question).
On top of that, many animals that make it into the tank have unknown habits and behaviors. For instance, tiny little coral crabs that come on ocean farmed or wild collected Acropora and Montipora corals. Not much is known about these animals, and not much is written about them. They're real cool though.
Another problem is that for some reason the hobby is in denial of certain supposedly "helpful" or "harmless" animals, that are supposed to have habits and behaviors that are "known", actually being animals that are either pests in some regard or another that have limitations in the home aquarium because of their many unknown or unforeseen habits and behaviors.
To complicate matters, these tropical marine organisms form a lot of very tight knit symbiotic behaviors with one another. Some of these symbiosis are understood well enough, others are very poorly understood.
Cool. A pic must be in order!
Corys breed easily when they mature. Sometimes they unexpectedly lay eggs that stick to the glass of the tanks.
Angels make good first time breeding fish, as far as egg layers are concerned as well.