Zipper? WTH? I never in my life had a pillow case with a zipper on it. 
The only thing I prefer is to have the tag of the pillow down in the closed end of the pillow case. Even that isn’t a “must” but a mild preference.
Seriously, I’ll have my eyes closed when you’re sleeping on it. None of this kind of stuff matters. I don’t even care if the sheets match, as long as they’re clean.
The zipper probably isn’t on the pillowCASE itself, but rather a separate pillow PROTECTOR which is usually an unadorned white cotton thing that goes over the pillow itself and under the case. You can use them to protect expensive pillows from getting grubby from hair oils etc. or some are made to block allergens (like dust mites) from getting into your pillows.
What she said.
Really? Now that I say it out loud, “orientate” does sound odd.
Nitpick: The Straight Dope. 
“…when I’m sleeping on it”. Gah!
As for the poll, I like to have the pillow tag (although I usually snip them off) or the zipper side of a pillow protector stuffed into the closed side of the pillowcase. Once on the bed I don’t care if the open end faces left or right.
TP, however, must unroll from the top. At work, if the cleaning lady puts the TP in backwards I will feel compelled to pop the roll out and put it back the right way because I’m just that crazy.
I also did vote for there’s something wrong with worrying about it.
This.
There’s no right or wrong on the toilet paper issue, but I can understand why people have their preferences. There’s no right or wrong on the pillowcase issue either, and I can’t even fathom why anybody would care one little bit.
The open end of the pillowcase should be on the side you don’t see when you enter the room, e.g. if you enter the room from the left, the opening should be on the right. That way a visitor isn’t traumatized by the sight of the naked end of the pillow.
And regarding the pillow itself: The end that contains a zipper or a tag should go into the pillowcase first, so it is hidden.
And the toilet paper comes over the top.
Yup, the “pillow protector” things that ugly ripe tomato mentioned. I didn’t know such things existed until I got married, but, oh boy, do I know all about the proper way to make a bed now. And by “proper” of course I mean “the way the missus wants it.”
I flip my pillows all the time. I don’t care which way the case is facing. One of my pillows (I sleep with 2 under my head) doesn’t even have a case. Don’t care.
But the TP should come down the front, so it’s easier to reach.
I suspect most of us don’t care one little bit, but that doesn’t mean there isn’t a right and wrong.
Man. In all my 51 years of living, I have never heard of such.
I couldn’t have a nekkid pillow on my bed. The scalp secretes oils and whatnot which make 'em yellow if they’re not covered.
Many years ago I worked in a hospital wing that was not air-conditioned. The nurses on the floor instructed me to place the open end of the pillow case facing away from the window, so that dust and pollen blowing in from outside wouldn’t lodge in the pillow and annoy patients with allergies. (As in, you could close their window and change their sheets, but it would be harder to get crud out of the pillow.)
But that’s a pretty specific and technical reason for anyone to have a preference.
I have two pillows, partially overlapping to sleep on. The open ends of the pillowcases are facing the outsides of the bed.
So, one right, one left. That better? 
I answered either is fine. I do, on the other hand, have to have my pillowcase opening away from the fan blowing at my wife’s face, otherwise it will inflate.
Even without the wind, I prefer pillow cases that button down.
(Be sure to have the pillow’s zipper on the inside. It’s not fun waking up with “YKK” imprinted on your face.)
kittenblue, we were separated at birth.
This is how my wife does it. She who makes the bed can arrange things however she wants. I like my pillow the opposite way (openning to the inside) so I flip it when I get in bed.