Mammalian kidneys do not regenerate nephrons, however a variety of bony fish do, including the common goldfish:
The full text of the abstract below is available here: http://ift.tt/18XnFdr this is the best review I’ve seen of the mechanics of nephron regeneration in these fishes, as well as prospects for nephron regeneration in mammalian kidneys.
Pediatr Nephrol. 2011 Sep;26(9):1435-43. doi: 10.1007/s00467-011-1795-z. Epub 2011 Feb 19.
Uncharted waters: nephrogenesis and renal regeneration in fish and mammals.