Using a mapping node to disable tiling is streaching texture? 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: