On a standard 6-string guitar, I always use my left thumb to stop the 6th (bass E) string when playing either the D major or the D minor chord. For the D major, I stop the string at the 2nd fret, raising the tone from an E to an F#. For the D minor, I stop the string at the 1st fret, raising the tone from an E to an F. Otherwise, I follow the standard chord charts. I also use my thumb to stop the 6th string on several other chords, including the F (1st fret) and the F# or F#7 (2nd fret).