Image textures with transparancy Help How can I mask an image?
I imported a downloaded image from CG textures that had the chequered background.
I converted it from JPEG to PNG.
I imported it into Blender 2.74 and later in 2.76 as an "Images as Planes"
Adjusted the "Import Options" to "Use Alpha" and " "Premultiplied" and "Emission/Transparent" but it still shows the chequered background when rendered.

I also did the long way with UV unwrap and "Transparent" nodes and Alpha noodle In Image texture to Mix shader "Fac"
In Blender transparent areas are not rendered as checkers... if you converted a jpeg that had checkered background to png, that does not make checkered areas transparent!! Your png has no transparency, I feel, this is why the checkers are always there...

You should either download that image again, but directly in a format that supports transparency (like png) or convert the checkered part of the png to a true transparent area...

In Blender if an image has supposedly transparent areas completely black or white, you can tell it to use those absolute colors to get transparency  (that is the purpose of "calculate" and "invert" options in the image texture  "image sampling" panel). "calculate" uses blacks in image to represent transparency, "invert" makes "calculate" use whites. 

This assumes your material and texture are set to be transparent, and the texture has some influence (>0) on material transparency.