There are many captive bred marine animals available now. Liveaquaria.com offers a bunch, in fact (that's where I buy my fish which is why I linked to it).
At the same time, plenty of freshwater fish are wild-caught. I can understand making the choice not to purchase wild-caught animals but it's definitely possible to have an "eco-friendly" marine set-up.
I agree with Stephanie. You can, if you try, buy a few species of captive bred marine fish. However, the majority of the big, showy species, like eels, sharks, angels and wrasses are all wild caught. If those are the kind of fish you are looking to get into, then you'll be buying wild caught fish.
You should be aware that even if you make the effort to look for captive bred, you're unlikely to find them in your local pet store. Few places, even on the internet, consistently have them in stock. Part of the reason is that the definition of captive bred is a bit murky. Gravid females taken from the wild that give birth in captivity are the source of some of these "tank bred" fish. Other times, I've seen shark egg cases collected from the wild. After they hatch, the sharks are called captive bred or tank bred. It's only a small step better than buying wild caught fish, but it's better than nothing.
Tropical (freshwater) are probably better than 95% captive bred. In most pet stores, it will be closer to 100% captive bred, unless they deal in very exotic and expensive species.
Sometimes the price of a fish can give you a hint as to whether it is captive bred or wild caught. In most cases, the captive bred marine fish will be the more expensive, whereas the wild caught tropical fish will be the more expensive.
The reason is that there are so few captive bred marine fish, that the breeders have very little competition from other breeders. They can command top dollar for their fish.
Captive bred tropical fish are the standard in the pet industry, so prices have to be kept low in order to stay competitive with other breeders. There are literally hundreds of tropical fish farms within a hundred miles of Tampa Florida. Only rare and high dollar fish are worth the trouble of catching in the wild. Some species of discus are a good example.
If you are looking to keep you costs low and to reduce your negative impact on the environment, captive bred tropicals are the way to go.
As far as marine invertebrates and corals, you can't be sure where it comes from. Even if they say it's cultured, it could be coral taken from the the wild. There is a significant amount of black market involving live corals (and the accompanying destruction of living coral reefs). It's very difficult to tell the good guys from the bad guys in that area, in fact, many dealers/importers could be dabbling on both sides of the law.
Sorry didn't mean to get so long winded, but I deal with fish importers/exporters on a regular basis. The numbers of wild caught marine fish and invertebrates that come into this country are incredible ...and alarming.