One of the most important collections of ancient fables are the verse fables by Babrius (Babrias, Gabrias). Not much is known about this poet; he lived probably in the second century C.E., perhaps in Syria or somewhere in the Middle East. Of his original collection containing approximately 200 fables, about one half have survived. There is an edition of Babrius by Ben Perry in the Loeb series, in a volume that contains the verse fables of both Babrius and Phaedrus; this book is invaluable not only for the works of these two poets but also for the enormous appendix in the back of the book which provides a complete guide to Perry's inventory of the Aesopic corpus.
For Latin versions of the fables, I have used the Greek-Latin edition by Jean François Boissonade de Fontarabie, which is available at GoogleBooks. He renders Babrius's Greek iambic verse very faithfully in Latin prose.