I have a writeup on glove boxes here: http://www.ilpi.com/inorganic/glassware/glovebox.html  See the section titled Bad Things

Speaking from the viewpoint of organometallics, there are two schools of thoughts on dry boxes.  One does most of the synthesis and manipulation of materials on high vacuum lines and keeps the atmosphere of the box pristine and void of solvents at all times.  You can sometimes spot the latter kinds of boxes because there is a small desk lamp set up inside and, if you look closely, you'll see that the incandescent light bulb in it has a small hole in it (made with a glassblowing torch) - it will glow despite the hole if the atmosphere is pure, but it the filament will burn out if oxygen or other reactive materials are loose in the atmosphere.

A couple anecdotes:

1. I was using a "wet" box rotavapping some solvent off a blood red reaction mixture. I apparently missed a small star crack in the flask, and it imploded, sending blood red material over every interior surface of the box.  I looked down at my hands, worked my fingers a couple times to make sure they were intact, breathed a sigh of relief and then set about the insane task of trying to clean the inside of a box without opening it to air using only paper towels, solvent, and tongs.

2. I had a student who apparently generated a shock sensitive material (not something we would have predicted offhand).  He had a few grams of it on a glass frit, picked up his spatula to scrape the material out and collect it, and it exploded.  The white powder turned instantaneously to black soot, and the entire front 1/4" Lexan panel of the box bulged outward about 2 inches. It had craze marks where it cracked slightly all around the perimeter. Definition near miss.  Incidents like this are why you should keep a clean pair of underwear in the lab.

3. One of the groups at MIT had a distillation or still running.  Overnight, the hose popped off the supply (probably not wired down securely), which I believe caused an issue with the still pot boiling dry.  The other issue was the flood.  The water went across the floor and shorted the pedatrol unit (see the link above, it sits on the floor and you tap one side to add nitrogen to the box when you pull your hands out and the other side to pump nitrogen out when you push your hands in).  It shorted the pedatrol on the inflate side, so the gloves started inflating until they eventually burst.  The lab occupants came in the next morning to find water everywhere, their still boiled dry, the arms of their dry box burst and flapping, and the contents of the dry box compromised.  All of this damage could have been prevented with a water flow monitor such as the ones at the bottom of this page (disclaimer: my company) http://www.safetyemporium.com/laboratory/heating-mantles/temperature-controllers/   Another way to prevent the pedatrol issue would be to raise the height of the pedatrol by screwing it to a small piece of plywood or such.

4. I was in my lab one day when the occupant of the lab next store came running in asking where the phone was, yelling something about a fire.  He starts phoning 911 so I ventured next door to discover that the cord of his glovebox pedatrol had caught fire.  Right in the middle of the ~6 ft cord, on a concrete floor, with nothing else within feet of it.  A flame all of 2" high. I put it out with a puff from the CO2 extinguisher.  So there's 2 lessons here.  First, a cord like that should be inspected once in a while as it is dragged around back and forth on a daily basis.  Second, no matter how much training you give people and no matter how smart you are (my labmate was part of a Nobel prize winning effort), in an emergency situation about half the people will either panic or freeze up, and the other half will respond in an appropriate fashion.  You need to get workers to role play in their head (or drill outright) what to do when an emergency happens so the response is both automatic AND appropriate.  I read somewhere that when a plane crashes, you have about a minute to escape and the people who do are the ones who had previously considered what they would do in the event of a crash (then again, I have to ask how do they know the dead guys didn't?).

5. It's best to have the glove box NOT be opposite a workbench.  I'm aware of one or more cases where a fire on the lab bench caused the glovebox across the aisle to be compromised when the gloves melted.  If you're one of the purist types who stores their man years of super-air-sensitive work inside a box, there is nothing more frustrating than losing all of your compounds and intermediates except perhaps losing all your lab notebooks.

A final note - a lot of organometallic folks pipe solvents directly into their boxes using solvent purification columns.  While this is far safer than the old school ways of distilling peroxide-forming solvents off sodium/benzophenone or Na/K alloy etc., you still have to pay attention to issues such as bonding/grounding etc.