Depends on what defines a Galaxy...
...if we're talking isophotal lines then the usual radius for the Milky Way when doing visible light galactic surveys is ~ 26.3 kiloparsecs (85.8 kilolight-years). If you're talking objects that are obviously gravitationally bound to the Milky-Way then there are galactic odds and ends out to ~ 300,000 light-years, including the Magellanic clouds (168 kly and 225 kly.)
So there you go. It's an arbitary line in the stars that the real galaxy doesn't really respect.
Adam