There are some non-classical carbocations, such as the 2-norbornyl cation, in which the positive charge is heavily delocalised. Have non-classical carbanions also been discovered? I have not seen any non-classical carbanions in books. If there are any non-classical carbanions, please provide some examples.
In addition to the species mentioned in the answer above, I found another one in Organic Chemistry by Morrison and Boyd(Seventh Edition)
Interesting question. It is much less studied and reported on than the case of non-classical carbocations, but I did find a few papers. Brown and Occolowitz (Brown, J. M.; Occolowitz, J. L. Chem. Commun. 1965, 376–377) reported that deuterated bicyclo[3.2.1]octa-2,6-diene 1b, below, undergoes base-catalysed de-deuteration (potassium tert-butoxide in DMSO) to give 1a much faster (ca. 3 x 10^4) than the bicyclo[3.2.1]octa-2-ene counterpart, ie. 2b -> 2a. They suggested this is evidence for the intermediacy of a 6π-electron, delocalised (non-classical) carbanion 3.
Much more recently, Brown reviewed and provided additional DFT computational evidence for stabilisation and charge delocalisation in these species (Brown, J. M. Aust. J. Chem. 2014, 67, 1296–1300).