Thought this might be good for a sticky.
Species often sold as indoor bonsai that are NOT suitable indoors:
Serissa (all species and cultivars)
Fukien Tea (all cultivars)
Moonjean Tea (Nashia inaguensis)
Gardenia (all commonly used cultivars)
Junipers (all species and cultivars)
Azalea (all commonly used cultivars)
Money Tree and Bamboo (Impossible to style)
Chinese Elm (all cultivars, virtually all species)
Some people have had a modicum of luck with Chinese Elms. The species is widespread and some individual trees do livem and are evergreen, in subtropical climates. However, the trees you buy for bonsai are NOT guaranteed to be subtropical stock. Most (virtually all) Chinese Elms kept indoors will languish until they attempt to go through cycles of dormancy and budding (sometimes both at once) in rapid succession, after which they will usually fail.