humbuckers often times don't have all those individual coils, it's not always a single coiled pickup, some are full blocks...
I think covered pups can help reduce microphonic feedback and external hum caused by other thing in the room (i.e. lights and stuff). They also mellow out the pickup more i believe, so reduce treble and harshness. But yeah like the guy above me said there isn't a whole lot of difference. You won't get totally revamped tone from covering/uncovering them, but you probably will notice a difference.
Some people say the uncovered ones have a clearer, brighter sound compred with the same pup covered. That might have been true forty years ago but not so much now. You listen to an old Goldtop with the mini buckers and it sounds as sweet as regular size with the covers off.
Pose value back then would be a different matter.
i think it reduces the attack of a pickup, but not a whole lot. a friend of mine thinks he gets more sustain out of his guitar with them, but i think he's crazy. they do reduce feedback though, and random noises like that guy said, and they look pretty.
There isn't much difference. I've experimented with both on my les pauls. It's definately not worth the effort to get out the soldering iron to remove the covers. If you do remove the covers, you'll also have to get rid of the wax underneath...

Now that I think of it, there is a difference with older pickups: My T-tops sounded a bit more trebly, but I didn't particularly enjoy the sound, so I just put the cover back on...
My Signal Chain:

Gibson 1974 Les Paul Custom
Vox AC-30 cc2 combo
JAM Pedals Tubedreamer +

Nigel will always be 1 louder than you!
Quote by TatarSalad2
It's to protect the coils from dust and debris, I believe.


Open Coiled ones tend to have there own covering. Its more of an aesthetic thing, than anything.
Quote by JesterShred
humbuckers often times don't have all those individual coils, it's not always a single coiled pickup, some are full blocks...

what the hell?

Humbuckers ALWAYS have 2 separate coils wound in opposite directions. That's what a humbucker is.

this should help with the question a bit http://www.youtube.com/watch?v=eZO5Olq5tqk up to the point where this guy switches on his nasty distortion which makes everything sound the same so the comparison is useless - his clean sound makes the differences more obvious (basically, at the start of the video).

It kinda changes the soft, smooth sound to a bit more of a raw, harsh sound, really.
Live Rig January 2018

Fender Baja Telecaster/Danelectro DC-12
Boss TU-3, Ibanez TS-9, Fulltone OCD 1.7, EHX Small Clone, MXR Carbon Copy, EHX Holy Grail Neo
1964 Vox AC30TB with '69 Rola G12M "blackbacks"
Elixir Nanoweb 10-52 strings, Dunlop Jazz III XL picks