The use of “helpmeet” indicates a failure to correctly parse the Jacobean English of the KJV. In the phrase “an help meet for him,” the word “help” is being used as a noun (“helper” in modern English) and the adjective “meet” (meaning “suitable”) heads the adjectival phrase “meet for him.” Adjectival phrases generally follow the noun, but single adjectives precede it, so that one says “an help meet for him” or “a helper suitable for him” but “a meet help” or “a suitable helper.” The fact that people don’t talk about “a meet help” shows that they’re not truly understanding what the KJV is saying.
Does it matter? Yes, because the misunderstanding changes the sense of the passage. The term “helpmeet” is often used by people arguing for a single model of femininity, and the passage actually states the contrary. Adam is given a helper (Hebrew `ezer, Septuagint βοηθόος) corresponding to him (Hebrew kenegdo, Septuagint κατ' αὐτόν). A “kind of counterpart,” as Calvin puts it. In other words different men are suitable for different women and vice versa. It is no accident that the catalogue of animals is inserted precisely here, because one man’s ideal complement is a lioness, while another’s is a pen, a hind, or a queen. Conversely, a doe will gain more joy by looking for a buck, rather than a boar.
There is also “no sense derived from the word linguistically or from the context of the garden narrative that the woman is a lesser person because her role differs” (Mathews). One of the most interesting practical illustrations of a “suitable helper” (albeit one from onother time and place) is The Treasure of the City of Ladies by Christine de Pizan, which explores the role of women in medieval French society, from the princess down to the peasant’s wife.
Update: See also the OUP Blog on the history of “helpmeet.”