Snail-eating fish usually cause more problems than the snails themselves.
In a well-maintained aquarium snail populations will stay relatively low, and physical removal of any excess isn't too onerous. Adding a few Assassin Snails can place a further break on snail population growth. But only if the aquarium isn't properly maintained will snails multiply so badly they become a serious problem. After all, all snails can do is turn organic waste (like uneaten food, algae and fish faeces) into baby snails. Keep a tank lightly stocked and limit food input will take care of the uneaten food problem; installing bright light and fast-growing plants will minimise algae; and light stocking, decent filtration and regular water changes removes fish faeces.
Generally tanks with snail problems also have other problems as well, such as unsightly algae. I've got a planted tank (nothing high tech, just carefully chosen plants under moderate light) and the snail population has been steady for many years. On the other hand, I have a tank with messy fish and no plant growth (several herbivorous fish in there!) and the snails breed like crazy. Since I can't do much about improving that tank, periodically I "blitz" that tank by removing all the substrate and replacing with new, while also removing as many snails as I possibly can while the tank is empty. If you can use a molluscide, perhaps with the fish removed to a quarantine tank, then so much the better, and your snail removal exercise will be dramatically more thorough. But you will still need to clean out the tank because hundreds of decaying snail corpses isn't helpful to water quality management!
The problem with snail-eating fish is that they often don't consume enough of the snails (especially Melanoides spp.) to justify their inclusion when compared to their shortcomings as community fish. Puffers nip fins or need brackish water; loaches are often boisterous and may need to be kept in groups, so you "waste" space on them instead of the fish you want; and cichlids that eat snails (such as Convicts) tend to be too aggressive to be worth keeping in anything other than a cichlid aquarium.
As mentioned by thereverendturtle, Assassin Snails can work well, but their impact is long-term rather than as a quick fix.
Cheers, Neale