(Note: The "former players" thing is just listing players who've been confirmed to have played in this league in the past.)
EuroBasket-Furr - European league. Teams include Falco-VI (Hungary).
(Former staff members: Dimi Kabat)
European Furry Basketball League (EFBL) - Europe's largest league. Has its own page on the Wiki.
(Former players: Daius Aurelias, Esmee Farai, Rytis Konstanblačkas, Ambrose Slade, Alessandro Serra, Blake Toivonen)
Furikorisliiga - Finland. Teams include the Manse Kommeetat.
(Former players: Otto Okkonen)
Furry Basketball League (FBL) - Australia.
(Former players: Kang-Dae Nabi)
Great Lakes Basketball League - Initially established in 1927, but folded in 1931 due to the Great Depression; reestablished in 1948 and lasted until it folded for good in 1978. Teams included the Hamilton Mariners, which was later absorbed into the FBA and later renamed the Albany Alphas in 1995.
(Former players: Brock Thiessen)
Russian Basketball Federation - Russia (well, obviously). Teams include the Vladivostok Predators.
(Former players: Vladimir Andreiovich Zhidkov)
Small Furs Basketball Association - Existed 2000-2003. A professional league restricted to players 5'4" and under. Ultimately folded due to the premise alienating too many potential followers (people were either expecting it to be comedic and disappointed, or were put off by the comedic-sounding premise).
(Former players: Michael Morgan)
(Mentioned: a league for arthropods created in wake of the five-limb rule; a college-level Euro league.)