Dorian Mode
The dorian mode is built on the second step of the major scale, using the same notes. For example, the D dorian scale is built from the notes of the C major scale, starting on D, and consists of "D, E, F, G, A, B, C". The dorian mode is a lot like minor scale, but the sixth step is raised a half step. That is, the D minor scale would have a Bb while the dorian has a B. Because it is so similar to the minor scale, it is natural to play this scale over a minor seventh chord. In fact, it is used more often than the minor scale itself. If you go to a piano and play a Dm7 chord ("D F A C") in your left hand, and play notes from the D dorian and D minor scales in your right, you will probably find that the dorian mode sounds better, because the B is less dissonant against the Dm7 than the Bb is. If you use the dorian mode over a minor seventh chord, there are no notes to avoid.
Like the major seventh chord, you can add more thirds to the minor seventh chord to obtain Dm9, Dm11, and Dm13. These chords still imply the same dorian mode. If you use the natural minor scale, the thirteen chord contains the note Bb, which is somewhat dissonant in this context. This chord is seldom used, but when it is called for, it is often notated Dm7b6, and is one of the few exceptions to the rule that most chords are written in terms of odd numbered extensions above the seventh. This rule comes from the fact that chords are traditionally built by stacking thirds. The notation Dm6 is sometimes as a synonym for Dm13 when the B natural is explicitly meant.