Other than the stereotypical grass skirt (which is not generally worn in Hawaii except by hula dancers), no pieces of clothing are more associated with the Islands than the aloha shirt and the muumuu.
The ever-present aloha shirt comes in a wide variety of designs. On one end, there are the brightly colored, tourist-oriented, polyester aloha shirts that many stores throughout the Islands carry. On the other end of the spectrum are the type of collared aloha shirts that have become standard business attire among career professionals in Hawaii, in the same way that the business suit is on the mainland. These aloha shirts are usually cotton-polyester blend and are "reverse print." Reverse print means that the design is printed on the inside of the shirt, resulting in a more muted, businesslike look.
For females, the muumuu is a long Hawaiian dress, usually made of cotton, that hangs loosely from the shoulder.
A special note on shoes: The item commonly referred to on the US mainland as a "sandal" or "flip-flop" (or more limited "thong") are called on the islands a "slipper" or "slippa". Using a mainland term for the shoe will get you a quizzical look from locals. Call them by their island name and they will instantly know what you are talking about.