Easier to answer what kinds are good....
The few reef safe species are far outnumbered by the predatory ones:
Most brittle and serpent stars found in the hobby are safe with a couple of exceptions. The larger green ones have been reported to eat fish. I have seen the large orange brittle stars grab small fish as well. Other species on occasion have been reported to eat fish however with no real frequency. I have never had a problem with dozens of different brittles and serpents I have kept. They will of course scavenge dead fish bodies and thus some probably get the blame for being fish eaters. I have had the best luck with the purplish-pink stars from the Atlantic, micro-serpent stars and the harlequin serpents.
Asterina sp stars. Most are harmless scavengers although there is apparently a (very uncommon) species that feeds on coral tissue.
Other than those, Linkia and Fromia sp. stars are usually reef-safe. They dont usually last long in smaller, newer tanks though and arent really recommended.
Just about every other starfish you encounter in the hobby is likely predatory and doesnt belong in a reef.