Generally speaking, no, Identify does not reveal curses. The DMG, in the section about cursed items, says: "Most methods of identifying items, including the identify spell, fail to reveal such a curse, although lore might hint at it. A curse should be a surprise to the item’s user when the curse’s effects are revealed."
Some cursed items countermand this in their specific case by noting that Identify does reveal the curse -- they say so explicitly where it does. Some also react uniquely to Identify, giving false information - the cursed items that do so say so specifically (for example, the stone of ill luck shows up as a luckstone when Identify is cast on it).
