Come Together is written in the key of E♭ Dorian.
According to the Theorytab database, it is the 8th most popular key among Dorian keys and the 41st most popular among all keys. The E♭ Dorian scale is similar to the E♭ Minor scale except that its 6th note is a half step higher (C). Chord progressions in Dorian have a characteristic sound due to the major quality of the chord built on the 4th scale degree.
See the E♭ Dorian Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!