Skinning carrots, cucumbers and potatoes isn't all that hard - I do it all time. Granted, their shapes go from roundish to squarish after I'm done, but the peel (and a lot of the vegetable meat) is off, so it works. Should you prefer your rounded vegetables to stay round, you can use this: the Rotary Peeler.
Created by Joseph Joseph, the contraption is designed to be cupped in your palm and applied to the surface of whatever fruit of the land you're peeling naked. Intended to cut through just the skin, it will preserve as much of the meat as possible, reducing waste and preserving the vegetables' natural shape. Yes, you never have to settle for square cucumbers again.
The Rotary Peeler includes three stainless steel blades that you can pick by simply adjusting the dial along the edge. You get one standard blade for carrots and potatoes, a Julienne blade for julienning the snot out of your celery and apples, and a soft-skin one for tomatoes and pears. Of course, they will work other fruits and vegetables too. Heck, you can probably use it to skin snakes, since those reptiles are round. Don't cringe - I heard they taste like chicken (if chickens were slithering serpents).
Joseph Joseph says the kitchen tool is ideal for both left and right handed vegetable gutters. It cleans easily too - simply unclip the case and take out the blades for washing. The dial includes a big eyehole for conveniently hanging onto hooks.
Future french fries, prepare to be peeled right. The Rotary Peeler doesn't appear to be available yet, but will be peddled in gray, pink and green when it does come out.