The following refers only to authentic Jelly Belly jelly beans. In no way does any of this refer to evil generic jelly beans or any other impostors.
PROPER CARE AND MAINTENANCE OF JELLY BEANS
Jelly Belly jelly beans are probably among my favorite foods. They mix well, they're sugary, and somehow they manage to taste like what they say they do. There are over fifty flavors at the time of writing, including some bizarre ones like Buttered Toast. And as I said, Buttered Toast somehow manages to taste like actual buttered toast, despite that it's quite obviously a little oblong dextrose package. Jelly Belly uses natural flavoring for this; I have yet to take a tour of the jelly bean factory, but basically it involves mixing the appropriate flavoring with gelatin and proto-beans. You can even mix jelly beans to produce new flavors: simple and obvious ones like Buttered Toast + Strawberry Jam, complicated but just as noteworthy ones like Top Banana + Chocolate Pudding + Crushed Pineapple + Strawberry Jam + Very Cherry + A&W Cream Soda (that's a banana split, by the way). The official site at http://www.jellybelly.com has a menu of the "official" flavors and combinations, and a menu is also included with some packages of jelly beans.
GENERAL ENVIRONMENTAL CONDITIONS
None of the above, however, addresses how to properly care for jelly beans. It is crucial that you keep them out of the sun and out of the cold, lest they become melty or frozen. If you pack them too tightly together there might not be any consequences, but it becomes all the more crucial that you keep them warm (not hot) and dry. Do not leave them out in the open for too long; while jelly beans can last for up to two days under optimal conditions without noticeable hardening, they do go stale around the third day, and you never know where flies might be. There's no harm in keeping them out and exposed in the short term, but you're better off wrapping them up for longer periods of time. Jelly beans in a closed paper lunch bag can last around four days, but if they are put inside a thin plastic bag which is then placed inside the paper bag, they can last for much longer. (I wasn't able to test for longer than eleven days due to hunger, but they did make it that far in good condition.) Covering a bowl or plate with plastic wrap is in fact not very effective; they only last about two or three days with this, probably due to the porous nature of the wrap.
The optimal temperature for a true jelly bean is between sixty degrees and seventy-five degrees Fahrenheit, or fifteen degrees and twenty-four degrees Celsius. Any less and the jelly beans may become hard and difficult to chew. When the temperature reaches about eighty-five degrees Fahrenheit (about 30 degrees Celsius), the jelly beans will become much softer than usual on the inside. Curiously enough, jelly beans don't melt in normal environmental conditions (up to about 110 Fahrenheit/43 Celsius)-- my guess as to why this is so is the hard exterior. Heat is much less of a crime to jelly beans than cold or wetness, although they may be a little softer and chewier on the inside than they should be.
In regard to extreme heat, jelly beans fare better than one would think. Once exposed to extreme temperatures of around 170 degrees Fahrenheit (77 Celsius) inside my toaster oven, the jelly bean did in fact melt. However, even at this temperature the jelly bean did better than I thought it would; after two minutes of exposure there was still no change on the outside. After three and a half the outside began to show stress and lightening at the edges, and when poked, it gave. The outside did not break, however, and it returned to its original position when the fork was withdrawn. After five minutes the outer shell was moving (was the inside bubbling?), and the fork punctured it. Had I left it to cool down after those five minutes rather than jabbing it with my fork, it might even have become hard again.
Freezing a jelly bean has predictable results; it becomes hard and cracks when one attempts to chew it. Eating a frozen jelly bean actually isn't bad, but it certainly doesn't have the texture it should; it more resembles hard candy than a normal jelly bean. I'll probably try and freeze some together at some point to see if it's possible.
Jelly beans should never, ever, EVER be put out in damp weather. If a large cluster of jelly beans (like a bunch of them in a bowl) are put out in damp weather or indoors near an open door on a rainy day, they can and will "pack." This is when they seem heavy and not as mobile in their container as normal jelly beans are, although poking or shaking violently will certainly move them. The outside is no longer hard-- it's firm, but not hard. (The difference between hard and firm becomes very apparent when eating damp jelly beans.) If you stick your finger in a bowl of "pack"ed jelly beans, you'll notice that the jelly beans seem reluctant to move (they will if you shake them), heavier than normal, and damp. They taste the same as ever, but the feel of the jelly bean is noticeably different. There is no real way to remedy this bizarre "pack"ing (and it does feel odd eating a formerly "pack"ed bean; it feels damp and icky) other than emptying them onto a paper towel and drying them all off. Having jelly beans out in damp weather is a bad, bad idea, even if it's for as little as half an hour. Take my advice and move them somewhere dry. If it's rainy out and your house/apartment/box is sticky, well, dammit, move them onto a DRY paper towel, make sure they're no more than one level deep, and run some airflow over them.* The continued survival of these jelly beans is critical.
Dryness is never a problem for jelly beans. Leave them out in zero percent humidity and they'll be fine. In fact, the dryer the atmosphere, the better. I'm not suggesting you go and take some desk fans to put on them, but you really should never worry about it being too dry out for them. Generally, under 40% or so humidity you'll see very little difference, but what you will see will be positive.
* If you don't have a desk fan with which to provide airflow, you can short an ATX power supply by connecting the end of the green wire on the motherboard plug (there's only one green wire) to a ground (any black wire), then hook a case fan (if you have a good 120mm one, that's best) up to one of the 12v connectors. You can even get away with shorting it with steel wire if you don't have any aluminum/copper wiring available. That should make the power supply turn on as soon as it is plugged in (well, and switched on if there's a switch on the back) without any computer necessary.
Keep jelly beans in temperatures no lower than sixty degrees Fahrenheit (again, 15 Celsius) and preferably no higher than seventy-five degrees Fahrenheit, although up to 84/85 Fahrenheit will probably be all right too (24 and 29 Celsius, respectively). The humidity should be no more than sixty percent or so, and if you plan to keep them for more than twelve hours, get a container of some sort. If you're using a tin to store them, try and make sure the tin is closed when not in use and that it is sealed tightly. If you don't do all of the above, you might end up with hard, soft, cracking, stale, and/or damp jelly beans. Eat responsibly.