The Court of the Crimson King is written in the key of E Minor.
According to the Theorytab database, it is the 2nd most popular key among Minor keys and the 8th most popular among all keys. Minor keys, along with major keys, are a common choice for popular music. The three most important chords, built off the 1st, 4th and 5th scale degrees are all minor chords (E minor, A minor, and B minor).
See the E Minor Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!