I'm having a bit of an issue getting started with UV mapping in Cycles. It works fine initially, but when I add the mapping node and set min/max to the default values to turn off repeating, I get the following stretch.
This is a bit boggling to me as I followed multiple tutorials where this exact same process works. See here
Images of the issue: 
As mentioned by Róbert László Páli, this is an artifact of the way the mapping node works.
You can get around this using hjaarnio's technique:
Using this node setup that creates a map of where the image is:
Values in the 0-1 range are where the original image is, so if we use that as a mix factor:
It will use the Image texture only where the original image is mapped, and Base Color everywhere else.
Base Color can be a texture or even another shader as well:
Enabling the min and max values for the mapping does the following:
When the coordinate for the UV is above the one
(when a certain point is above the image on
the UV) then it changes that value to one.
So the sampler will sample a pixel from the coordinate one, which is the topmost pixel of the image (and also the zero value is sampled from there). So for every point that is UV-mapped above or below the image, the color will be from the top row of the image. The same applies to the other direction.
A dummy solution would be to add one pixel transparent black border to the image to achieve a decal on the mug. But you have to use the alpha channel to mix the image with the original color.
