I've only ever used side chain triggering for compressors acting on drums. Where a kick signal compresses snare and toms. I'm trying to figure out some interesting use cases for side chain compression on a guitar or bass signal. What would a typical side chain trigger be for these instruments? What context would I use this kind of side chain triggered compression on guitar or bass under?
There are a few scenarios that spring immediately to mind:
If the overtones (or fundamenals, really) of your guitar or bass are in the same range as a vocalist, you can use the vocal signal as the sidechain input, "ducking" those instruments out of the way during vocal passages. I tend to think this works better for more rhythmic vocals, although I don't have a whole lot of experience to back that up.
Of course if you're making French House music you can always compress half of the mix with a kickdrum sidechain, which makes everything nice and bouncy. :)
As Zerodyne said, a gentle compressor on a bass triggered by the kickdrum can allow the kick to punch through the bassline a little better, without necessarily having to EQ out the common frequencies from one track.
You can also use it for making simple guitar-synth effects as well - use a heavy compressor with a long release time to make the sound ramp up, and use a controller to trigger a drum sample that isn't in the mix, but is used as a control for the compressor. You can strum a chord at the same time as one of these triggers, and you'll hear the chord rise in volume as the compressor releases. This technique generalizes to many kinds of instruments, although it's definitely an "effect" rather than a natural sound.
If you have a bass line that is closely (or exactly) mirroring the kick drum, triggering the bass compression with the much sharper attack of the kick can tighten up the line. Even if you push it to the point where it sounds unnatural, it can still be very musical.
For both guitar and bass, it's fun to trigger a gate with a different signal. The last time I did this, which was years ago, I had a washy guitar sound with tons of delay playing chords, and the bass was opening and closing an extremely tight gate. It sounded a bit unpleasant dry, but with a little overall reverb softening, it was striking and effective.