Recently I'm finding that I'm ending up using only part of a bell pepper for a meal, and so wish to store the rest for later.
So how should I best store half-used bell peppers so that they stay as fresh as possible?
Put in a ziplock bag with a piece of paper towel to absorb moisture, and stick in the fridge. Also applies to lettuce.
Bell peppers suffer from cold storage stress: their respiration rate goes up when they are stored in a cold place, which makes them spoil faster. One trick to get around this is to dip them in warm water (130°F / 55°C) for a few seconds (12 on average), dry them, and store in the warmer parts of the refrigerator wrapped in a paper towel and in a ziploc as @Tim Gilbert explained.
Due to general time constraints after work right now, I actually purchase all my peppers in bulk and freeze them.
I take a Saturday or Sunday and cut them all into a combination of strips and dices, freeze them on baking sheets in our second freezer (my home version of IQF), and then store them in ziploc bags in the kitchen freezer for easy use. When a recipe calls for any kind of peppers, onions, or garlic, I just reach into the freezer and grab a handful. Because they're frozen individually they don't stick together, so they're easy to portion, and since I generally sautee them anyway, they defrost extremely quickly in the pan (or in a casserole as it bakes).
My wife prefers the texture of frozen-then-cooked onions to fresh-cut onions; I personally don't have a preference, both are just fine to me.
I cut the pepper along it's "seams" and around the "shoulder," discarding the center with the seeds. Then I trim the membrane from each section and discard. I stack the sections, skin side down, in a large enough plastic container (I use a clean Cool Whip container.) to hold them without hitting the lid. I use chopped green pepper in my salads and the pepper has lasted two weeks or more.
I only cut what I need keeping the center with the leftover parts and put it in a plastic container like a sour cream container in the fridge. Never had any problems with it staying fresh, but I do go through peppers pretty quickly (i.e. once cut it is in the fridge at most two days).
I've got some Tupperware Fridgesmart and I think they're great. The peppers & lettuce last so long and keep so well.
Disclaimer I don't work for or receive any commissions from Tupperware (though my cousin is a rep)