There are two situations: transition chords going from one main chord to another, and varying a main chord which goes on for a while.
Here are several simple tricks to vary the sound of a prolonged harmony:
- Alternate between different voicings of the chord (moving it higher or lower on the neck).
- Alternate between the regular chord and a "suspended" alternative: D - Dsus2 - D; or G7 - G7sus4 - G7. For 7th chords, alternating with 9ths works well, too.
- Shift the entire chord up or down by one fret, then return: A7 (2434) - G#7 (1323) - A7. During singing, these shifts should be of brief duration (a beat or half-beat), or they'll clash too much harmonically.
- For a major or minor triad, temporarily add a 6th or major 7th: D - D6; or C - CM7 - C
- Switch temporarily to a new rhythm, particularly one broken with silences, or use a special strum technique like rasgueado or a triplet.
Remember that sus chords are neither major nor minor, and thus substitute for either major or minor chords: Dm - Dsus2 (2200) - Dm.
Transition chords are harder to generalize, since they depend so much on the bracketing chords and the playing style. But here are several common approaches (also used in turnarounds):
Follow the circle of fifths to the ending chord. To go from C to D, you can jump from C to the chord two steps beyond D (E) and follow the circle backwards to D: C - E(m)7 - A7 - D. You can make this more interesting with dominant alternatives like 9ths, b5s etc.: C - E9 (1222) - A9 (0102) - D6.
Step either the start or end chord shape chromatically up or down to the end chord. Sometimes I change chord shapes in the middle of this kind of chromatic progression, such as in this A7 to (higher) A7 transition:A7 (2434) - A#7 (3545) - [shape change] G#7 (5646) - A7 (6757). The interior change works especially well because the ear gets harmonically disoriented by the leading chromatic shift, but because the last two chords are so alike, the change in chord quality is masked—it seems to occur by magic!
Interpose an ambiguous chord, like dim7. These are like musical roundabouts: you can enter them from almost any direction, and come out in almost any direction. Ambiguous chords can also be chromatically shifted to good effect.
Use a single note to step up or down between the chords, either chromatically or diatonically. Most usually, one steps between the roots or lowest notes, but you can also step between the top notes of each chord or any other inner voices. Let instinct guide you here; you'll probably hear in your head what kind of stepping would work well in a given case.
Of course, in either situation (static chord or chord transition), you can drop in a short melodic riff. This simple expedient can greatly improve one's playing (I say, as someone who doesn't do it nearly enough).
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