Colorforms.

The Colorforms company started in 1951 and they are still going strong. Today you can buy Dora the Explorer and Fancy Nancy Colorforms. In my day you could find the Smurfs and Holly Hobbie.

A description from Wikipedia:

Colorforms, invented by Harry Kislevitz, are toys produced by the Colorforms Corporation. Colorforms are paper-thin, die-cut vinyl sheet images and shapes that can be applied to a slick cardboard background board, much like placing paper-dolls against a paper backdrop. The images stick to the background via static cling and can be repositioned to create new scenes. The original box sets began appearing in the 1950s and feature bright shapes and "modern" basic designs, expanding into cartoon character sets. Later Colorforms licensed various properties, producing box sets supporting various TV series and movie releases.

I think I had more than one kind of Colorforms, but the one I remember best was the Little House on the Prairie set pictured here.

Colorforms, 1979

I no longer have my ultra-cool Colorforms set, but this one can be purchased online for a mere $120.00. Yikes!