In my first few months here in UK (back in the mid-90s), I missed Asian food so much that I was always scouring the aisles of our local supermarket for anything mildly Oriental or Southeast Asian. You could just imagine my delight when I saw a stack of fresh pineapples (pinya or piña in Tagalog/Spanish) in our local supermarket. What's more, it's got a sign saying that they will peel it for free. I thought that would save me a lot of effort and time so off I went and bought one. The lady on the counter got my pineapple, chopped off the top and bottom, sat it on a metal contraption with a big lever. Then she got hold of the lever pulled it down in one big motion - whoosh! Out came my pineapple in a perfect cylindrical shape with a hole in the middle looking exactly like what you get from cans. Well, at least it was done in no time at all but I have to lament the large amount of wasted pineapple! I'm one person who hates waste and I was just flabbergasted with how much was taken off it.
As an alternative I'll show you how pineapple is peeled in the Philippines wherein you can get the most out of your 'multi-eyed' fruit. See the series of pictures below on how you can peel your pineapple. It may take a bit more time but the satisfaction of having a more aesthetically pleasing and less wasteful way of doing things will surely encourage you to try this.
[Click on the pictures for a bigger view]
If you notice the eyes are arranged by nature so that they have natural diagonal alignments. The lines they form are either slanted left to right or right to left. Choose one of the lines to follow (I usually take the less slanted one). Now, connect the eyes along the line that you chose by making a V-shaped canal with your sharp knife (usually you connect two eyes at a time).