The harmonic minor scale is a great device for creating full-blown shred licks a la Paul Gilbert and Yngwie Malmsteen. I'm going to present some of the basics here, but my good buddy, Craig Smoot, has a neo-classical shred lesson in the works which will take it to the next level.
The examples in this lesson will all use the A harmonic minor scale which is great for tunes based in A minor. The notes for the A harmonic minor scale are:
Note how there is a 3 fret difference between the F and the G#. This is what gives the harmonic minor its characteristic sound. You might think of it as a natural minor scale (or aeolian scale) with a natural 7th (in this case, G#) instead of a flatted 7th (G). Listen to the example below, which shows the fingering for this scale in root position with 3-notes played per string: