There are two ways to pronounce the noun conch—which refers to a variety of sea mollusks and their large shells—and how you pronounce it determines its plural. The more common pronunciation is with a hard k sound at the end, so that the word rhymes with honk. For this pronunciation, the plural is conchs. The other pronunciation is with a ch sound at the end, so that it rhymes with launch (in U.S. pronunciation, at least). The plural for this pronunciation is conches.
The word exists in many forms across a number of languages and has a long history going back through Latin and ultimately to Greek.1 Reflecting these various influences, the word has taken several spellings over its approximately six centuries in English, and several pronunciations are justifiable from an etymological standpoint (which, in any case, is not how English pronunciations are decided).2 Both conchs and conches appear in writing from as far back as the early 18th century (see below for some historical examples), which suggests that both pronunciations have been around for at least three centuries.
The Conchs, some of these are very large, but the lesser sort are the best Meat; and that, in my Opinion, not extraordinary. [The Natural History of North-Carolina, John Brickell (1737)]
On the South Sea coast are some small shell-fish, or conches, peculiar to it, and perhaps the most beautiful in the world. [The Modern Part of An Universal History (1783)]
Shells or conchs, to which are affixed (with some ingenuity) mouth-pieces of carved wood, are also prized by the people. [Manners and Customs of New Zealanders (1840)]
A woman in one of the settlements on Abaco was one day taking some conches out of their shells; while so engaged a duck seized one of the fish (culinary operations are all carried on in the open air), and ran off with it, pursued by the woman. [The Nineteenth Century: A Monthly Review (1888)]
Very highly ornamented shells exist in the Trias, but following this period the conchs are smooth. [Text-book of Paleontology, Karl Alfred von Zittel (1902)]
At night they would move out to the grass flats where the algae grow and forage for mussels, clams, and immature queen conches. [Popular Science (1969)]
For molluks, shells are practically de rigeur: snails, conchs, and chitons all sport shells with varying amounts of bling. [Scientific American (2012)]
As dawn broke over the Mayan ruins of Chichen Itza in Mexico, thousands of mystics, hippies, druids and pagans celebrated with crystal skulls, ceremonial fires, drums beating and conches blaring. [Telegraph]