My favorite, or at least most frequently used, is an octave down... maybe that's not entirely true, I use a slight detune (about +5 cents one side & -5 cents on the other) the most.
Other than that, 4ths, 5ths, 6ths, 3rds, octaves many combinations, up or down, diatonic with either a custom scale or in the key (or related key) of the song. Sometimes, in combination with a delay (like Ballerina by Steve Vai), sometimes a reverse delay (Crystals). I can get more specific in you'd like, but without knowing what you're using, I'm not sure that the exact parameters would match up.
As for gear, I'm running an Eventide H3000DSE and a GTR4000 w/DSP expansion card in my huge rack, an Eclipse in my small rack, and a Pitch Factor that I sometimes add to my pedalboard. While others can do it, for me, there's nothing better than an Eventide.
