Genius Of Love is written in the key of D Mixolydian.
According to the Theorytab database, it is the 5th most popular key among Mixolydian keys and the 30th most popular among all keys. The D Mixolydian scale is similar to the D Major scale except that its 7th note (C) is a half step lower. Mixolydian chord progressions are heavily featured in many genres of music like classic rock, which relies on the major chord built on the 7th scale degree.
See the D Mixolydian Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!