To make it simpler, it would suffice to list the families including finless (= without pectoral and/or pelvic fins) members (or taxa of higher level, if all the included families include finless species). I may start with a few examples that hastily occur to my mind: Ophichthidae (and several other families of Anguilliformes), Synbranchidae (Synbranchiformes), several families of Pleuronectiformes (e.g. Achiridae).