I got this Mario doll for Christmas in either 1989 or 1990. It was about a foot high and everything except for his face, hair, and hands were made of stuffed fabric.
New Super Mario Bros. Plushies
This is a collection of New Super Mario Bros. plushies released by Corgi Classics Limited. So far, I've seen plushies for a Super Mushroom, Mario, Petey Piranha, Goomba, and a Boo. I'm sure there are others.
Little Buddy Piranha Plant Plushie
This Little Buddy Piranha Plant plushie came out in 2013. Its stem is stiff though bendable so one could get the head to pose in various directions, either straight up like the classic 8-bit Piranha Plant enemies or facing sideways like in more modern Mario games.