No problem.
Actually it's thought they (american eels) may die once they go out to the ocean (the Sargasso Sea exclusively) and spawn, since they haven't been recorded migrating back inland, but it's not proven as far as I know. They stay inland in freshwater for 5-15 years before they go back to spawn. In captivity they can be kept freshwater forever, and in fact I'd assume (haven't researched it) that if you convert them to saltwater as adults it may trigger spawning behavior and death. In captivity in freshwater they can live over 40 years (43 max recorded), and a european eel (another anguilla sp.) was reportedly kept for over 80 years.
Lampreys are neat creatures for someone interested, but they're very specialized, and the other problem is many of them are endangered and threatened in various places. I don't have anything against them in general, just didn't think that's what the OP was going for.
One I forgot to mention is a siren. Not technically an eel, but an amphibian with gills, undersized front legs and no back legs. They're not especially hard to keep or feed, but you don't want to keep them with any fish that may pick on their gills.
I'm going to try to net one tomorrow in the ditches and I'll take pics if I find one. They're very prevalent around here. My friend rakes them up constantly when he's collecting crawfish.
I know in some states they are illegal to collect, but you can find them online periodically.
Are those legal here in Mo.?