Pear (Pyrus communis L.) is consumed as fresh fruit, in numerous food products, and also used as a traditional remedy in various countries, including Serbia. In search of bioactive compounds, six traditional pear varieties (‘Vidovača’, ‘Lubeničarka’, ‘Karamanka’, ‘Jeribasma’, ‘Lončara’, ‘Takiša’) and wild pear from Serbia were investigated and compared with a commercial variety (‘Williams Bartlett’). The aim of this study was to determine the total phenolic and flavonoid contents, phenolic composition, antioxidant capacity, and antineurodegenerative activities of methanolic extracts of peel, flesh, and mixed peel and flesh of pear fruits. Phenolic composition of extracts was determined with HPLC-DAD, while the antioxidant activity of extracts was evaluated by 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) (ABTS), and ferric-reducing antioxidant power (FRAP) assays. Bearing in mind that oxidative stress is closely linked to neurodegeneration, the antineurodegenerative potential of the extracts was assessed by the inhibition of acetycholineserase (AChE) and tyrosinase (TYR) activities. The extracts of traditional varieties, particularly peel extracts, had a high content of phenolics, as well as significant antioxidant and moderate antineurodegenerative potential, compared to the commercial variety. The highest contents of total flavonoids and individual compounds, such as arbutin and chlorogenic acid, as well as the strongest antioxidant and TYR inhibitory activities were reported for the ‘Takiša’ peel extract. The performed analyses have revealed that fruits of traditional Serbian pear varieties are rich in bioactive components and could be used as functional food and for possible nutraceutical applications, to prevent diseases induced by oxidative stress.