In world war two most of the major warring nations all had their own shoulder fired recoilless weapons. As far as I know the only ones that didn't were Italy, Japan and the USSR. Considering Italy had some major problems in industrial output it doesn't surprise me that they never produced one. Japan doesn't surprise me all to much either considering the lesser presence of armour in the Asian theatre.
What does surprise me though is that the USSR didn't have one. Why did one of the biggest and eventually best equipped armies not have their own recoilless rifle? What was their alternative? Were Soviet soldiers more regularly equipped with anti tank guns? Or did they have different tactics for taking on enemy tanks?
USSR had 65-mm anti-tank rifle prototype designed in 1931 by B.S. Petropavlovsky. http://s104.photobucket.com/user/Von_poop/media/album%202/sovietbazooka.jpg.html
However, main problem was that during 1930-1937 all Soviet artillery designs wer governed by one man - L.V. Kurchevsky, who was an avid proponent of recoilless artillery. But due to bad designs (and Soviet manufacturing quality) all of his projects were unusable.
So after he was arrested and killed in 1937, all mentions of recoilless system were met... let's say with a dose of disbelief.
First US-made bazookas were sent to USSR by lend-lease program, but since first models were not so reliable (as noted by US troops as well) a shift in attitude was only when Red Army met German 'Panzerfausts' in action and saw what they can do.
edit: grammar