The coelacanths are, of course, best known to most people for the discovery of the living Latimeria chalumnae in 1938 in South Africa, after the lineage had been thought to have become extinct in the Cretaceous. The subsequent media frenzy must have been interesting to fishermen in the area who had long known the coelacanth primarily as an infernal nuisance. Though only captured occasionally as bycatch, a landed coelacanth represents two metres or more of snap-jawed bad temper, while the oily flesh is inedible. More recently, a second species of living coelacanth, Latimeria menadoensis has been described from near Sulawesi in Indonesia.
Because of the circumstances of its discovery, Latimeria became a textbook example of a 'living fossil'. However, all fossil coelacanths were not mere duplicates of Latimeria. To begin with, Latimeria is quite a bit larger than the majority of its fossil relatives (Casane & Laurenti 2013). These included such distinctive forms as the fork-tailed speedster Rebellatrix and the eel-like Holopterygius. And then there was Allenypterus montanus, a Carboniferous taxon that... well, just look at the thing (photo from here):
Though Latimeria may lord it over its immediate relatives, it is far from the largest sarcopterygian (even excluding the tetrapods). The tetrapod stem-group also included a number of large predators, including the famous Eusthenopteron (how many other fossil fish have been referred to by name in an episode of Doraemon?). Particularly dramatic were the Rhizodontida, freshwater ambush predators of the Devonian and Carboniferous. Though probably very low on the tetrapod stem (and hence not directly related to limbed tetrapods), rhizodontids developed enlarged pectoral fins that articulated with the body in a not dissimilar manner to tetrapod forelegs. Like tetrapods, rhizodontids probably used their pectoral fins to push against the substrate and provide explosive propulsion (Davis et al. 2004). The jaw of rhizodontids contained enlarged tusks interspersed among smaller teeth that would have hooked into struggling prey. The largest rhizodontids have been estimated to be about seven metres in length, and were the sort of predator that the term 'apex' was invented for.
Casane, D., & P. Laurenti. 2013. Why coelacanths are not 'living fossils'. BioEssays 35: 332-338.
Davis, M. C., N. Shubin & E. B. Daeschler. 2004. A new specimen of Sauripterus taylori (Sarcopterygii, Osteichthyes) from the Famennian Catskill Formation of North America. Journal of Vertebrate Paleontology 24 (1): 26-40.
Zhu, M., W. Zhao, L. Jia, J. Lu, T. Qiao & Q. Qu. 2009. The oldest articulated osteichthyan reveals mosaic gnathostome characters. Nature 458: 469-474.