This is my favorite (true) eel: the Fangtooth Moray! They're known for their horrible glass-shard like teeth. However, like other eels, their jaws aren't used for tearing food. They're only for catching, so the eel's pharyngeal jaw (second, smaller jaw) can pull food whole down the eel's throat.
And for my favorite (non-true) eel: The Electric Eel! Despite its name, the electric eel isn't actually an "eel", but rather a freshwater knifefish. Although other animals, especially those in the same order of knifefish, can generate electricity similar to the eel, the electric eel is the most well known and is, in my opinion, one of the coolest and cutest.