Fairy and flasher are active, colorful, and completely reef safe. All of the flaher wrasses are quite peaceful. Most of the fairy wrasses are peaceful, though there are some that will be aggressive toward other wrasses. Both groups are quite hardy.
Halichoeres is a large genus that varies as far as suitability for a reef. Most of the smaller species, such as melanurus and chrysus, may eat small snails and hermits, but also eat coral pests. Larger Halichoeres species can be more aggressive and more likely to flip corals and eat larger inverts. These are sand burying wrasses.
Leopards, Anampses, and Pseudojuloides are peaceful, usually completely reef safe, and will eat coral pests. However, they don't handle shipping stress well, and are sensitive their first few weeks, but can develop into quite hardy fish. They do best in an established reef. They are all sand burying wrasses.
The lined wrasses of the genus. Pseudocheilinus are hardy and full of personality, but can be aggressive to small fish added after them, especially other wrasses.
Cleaner wrasses can have a role in aquaria, but do best in lg systems that are heavily stocked with fish, so that there are an adequate number of client fish so the cleaner doesn't become a nuisance. The genus Labroides is reef safe, the other generas of cleaner wrasses will eat corals.
Wetmorella and Pseudocheilinops are small, peaceful, cryptic species.