Garlic presses present a convenient alternative to mincing garlic with a knife, especially because a clove of garlic can be passed through a sturdy press without even removing its peel. The peel remains in the press while the garlic is extruded out. Some sources also claim that pressing with the peel on makes cleaning the press easier.
Garlic crushed by a press is generally believed to have a different flavor from minced garlic; since more cell walls are broken, more of garlic's strong flavor compounds are liberated. A few sources prefer the flavor of pressed garlic. Raw-foods chef Renée Underkoffler says "a good garlic press makes dealing with garlic a clean pleasure. Pressed garlic has a lighter, more delicate flavor than minced garlic because it excludes the bitter center stem. The magazine Cook's Illustrated says "a good garlic press can break down cloves more finely and evenly than an average cook using a knife, which means better distribution of garlic flavor throughout any given dish."
On the other hand, some chefs say garlic crushed in a press has an inferior flavor compared to other forms of garlic. For instance, chef Anthony Bourdain calls garlic presses "abominations" and advises "don't put it through a press. I don't know what that junk is that squeezes out of the end of those things, but it ain't garlic. The British cookery writer Elizabeth David once wrote an essay titled 'Garlic Presses are Utterly Useless'; Alton Brown has expressed suspicion towards them on account of being "unitaskers" for the most part.
Cook's Illustrated lists some additional uses for a garlic press, such as mashing other small items (including olives, capers, anchovies, and canned chipotles) or pressing out small quantities of onion or shallot juice.