My ideas and thoughts by circumstance:
1) relatively flat area, no bunker to carry, but 5-12 feet off the putting surface? I use a 3-iron hybrid with a putting stoke. Think of putting the ball about slightly less than halfway to the hole. Works a charm. Almost feels like cheating.
2) just off the green, within a foot or two of the fringe, but ball sitting down a bit in long grass? I take a wedge and deliberately hit the ball slightly above the equator. A purposeful skull shot, if you will. It looks weird and it sounds difficult, but in truth it is really quite simple and it only takes a tiny bit of practice to get pretty good at it.
3) Further than 10-12 feet off the green, thickish grass that seems unpredictable for rolling through? Traditional chip. I use the technique in the Kisner clip.
4) bunker to carry, short-sided? I use a sandwedge and just try to get the ball high up in the air as quickly as possible.