Why should/shouldn't I store my bread in the fridge/freezer/breadbox/plastic bag/etc?
Storing bread in the freezer you can store for several days and keep it soft.
To eat, remove from the freezer and put in the oven.
Bread in the freezer will stay edible for a long time. Freezing doesn’t much affect the texture of the bread either. The downside is that you have to thaw or toast the bread before you can eat it.
Bread in the refrigerator will keep longer without going stale or moldy. The downside is that the texture of the bread changes when it is refrigerated. I notice it quite a bit, but my wife doesn’t seem to.
Plastic is a good way to keep bread on the counter, but you want to make sure that it is completely cool before wrapping it. If the bread is still warm, the plastic will trap the escaping water vapor and the bread will get soggy.
Warm fresh bread should be allowed to (at least mostly) cool either on the counter or in an open bag. Once it is mostly cool, a paper bag is a good way to keep it if you need to put it in something. Any remaining water that is going to come out of the bread won’t pool up on the bread’s surface like it would while stored in a plastic bag.
For artisan bread, I usually wrap it in aluminum foil and keep it on the counter. I don’t have any reason to believe that this is somehow better than other methods. It goes stale after a couple of days, but if it’s not eaten by then we will toast it or make French toast for breakfast.
Bread goes stale in the fridge as you are storing it at the quickest stealing temperature. The moisture migrates in the starch from alpha to beta cells. You should never store bread in the fridge. Trust me I used to be a baker and it was one of the first things we learned at college in baking technology. The fridge will inhibit mould but pointless if it is stale. You can pop the bread in the oven for short while which will temporarily migrate the moisture back restoring freshness.
The best way to store bread I have found is in a good stone container that is keeps airtight. The stone container keeps the bread away from light and keeps the bread in normal temperature. It also keeps mold away very good, especially when washed every now and then with diluted lemon juice or vinegar.
The freezer is absolutely the best place to store bread you want to keep for more than a day or two (depending on the bread - baguettes keep fresh for only hours, multi-grain sourdough for much longer). Suck the air out of the bag so it doesn't get frosty, and slice before freezing if you want to use it by the slice. A few seconds in the microwave and the previously-frozen slice will be in very good shape. This won't work as well for something really crusty - the crust will lose it's crunch - but you really can't keep crusty bread long no matter what you do.
Don't keep bread in the refrigerator. It will go stale and get moldy quickly.
If you take the danish "rugbrød" (I think the closest english version is rye bread)...it gets really hard, dry and dull tasting if you put it in the fridge, though it'll be able to keep of the mold for a while longer.
Best way to store bread, including baguettes, is in the freezer where it can keep for months. Reheat by placing straight into a hot oven from the freezer. The bread will crisp up and be just as if you had just baked it. Bread that has gone a little bit stale can be lightly moistened with water all the way round, then placed in a hot oven to crisp up. Never store in plastic if possible. A thick brown paper bag will keep it pretty fresh on the counter for a couple of days. If you don't get through a loaf that quickly, it's worth freezing half.
I've always stored my bread in a dry, dark cupboard or drawer. I would assume that a bread box would accomplish the same thing. Bread stored this way has generally lasted me 2 weeks before mold even begins to start growing.
Another thing to keep in mind is to keep your bread stored in an airtight fashion. If you don't, you risk your bread drying out quicker.
My experience with keeping bread in the fridge results in faster molding, and dryer bread.
My favorite place to store bread is in my mouth/tummy :P
On a serious note: we've tried storing it in various places and each seemed to have enough downsides (coupled with how much we enjoy good, fresh bread) that we decided it was worthwhile to just buy and make it more frequently then it was to try to preserve it longer.
I bake bread frequently and store it upright on the cut end on my breadboard. It's a crusty loaf and the crust will get soft if wrapped. It doesn't last long in our house so long term storage isn't a problem. There is a way to restore the crisp exterior if you must wrap it in plastic. Preheat oven to 375 degrees Fahrenheit. Sprinkle a little water on the loaf or pat it with a wet hand. Place on the middle oven rack for a few minutes. It will crisp up almost as much as when it was fresh but it must have had a crisp crust to begin with. This doesn't work on the fluff from the supermarket.
Bread lasts longer out of the refrigerator.