Within Europe, the Marbled Swamp eel, Fire eel, Lesser spiny eel, Zebra spiny eel, Zig Zag eel, European eel
Zebra Moray, Yellowhead Moray, Yellow Spotted Moray, Yellow Edged moray, Yellow moray, White Ribbon eel, Undulated moray, Turkey moray, Tiger reef-eel, Tiger moray, Spotted moray, Snowflake moray, Ribbon moray, Reticulated moray, Purplemouth moray, Pink lipped moray eel, Peppered moray, Mediterranean moray, Leopard moray, Laced moray, Jewel moray, Hourglass moray, Honeycomb moray, Greyface moray, Green moray, Golden tail moray, giant moray, Geometric moray, Freshwater moray (g. polyurandon), Freshwater moray (g. tile), Dwarf moray, Dotted moray, Dark moray, Chain moray, Brown moray, Barred moray
Tiger snake eel, Harlequin snake eel, Goldspotted eel, White spotted garden eel, Spotted garden eel, Orange barred garden eel, European conger, and Band tooth conger are kept.
34 moray species alone, 14 other eels, 48 total is actually not nearly as bad as I thought. While most are only kept at a handful of institutions, many species definitely seem sustainable. Eels may be more commonly kept, at least in Europe, than we are discussing.
Does anyone have information about the population in the US? I'm pretty sure it will only be a small fraction of Europe's