In 1995~1997 maybe I had a few plush puppies. My dad gave me the set of 'em for birthday.
There was a usual plastic box where you could see the cardboard dog house for three puppies - one in the every dog house.
All the puppies were down on their stomachs. They were nearly flat. I mean, not really flat, but... Ugh... I don't know how I to describe that even in Russian.

I often saw that kind of toys until 2000 or 1999. Maybe someone remember what was that?
I think that was a cartoon show about that puppies too. In Russian it called "Backyard Puppies" or something like that, but I don't even know if the plushies and the show were related in some way.
I want to remember the name of that show anyway too.

I believe you're referring to Pound Puppies. I don't recall them having their own show, but I do still have a few of the little stuffed ones. =D

Hope that helps.

Yes, thanks a lot!
Now I'm really interested what was the show name... Hmm.

There were some cartoons, that were about dogs. Maybe you're mixing your memories of one of those up with your memories of those toys?

RHERE WAS A CARTOON ON ABC FOR TWO SEASONS CALLED POUND PUPPIES

Yeah there was. I remember watching it with my little sister. It was on every Saturday morning. They even ran it on the USA Cartoon Express at one time after it became syndication.

Retro Junk article of the show:
http://www.retrojunk.com/details_tvshows/25-pound-puppies/

And of the movie that came out first:
http://www.retrojunk.com/details_movies/1879-pound-puppies-and-the-legend-of-big-paw/

Hm... It wasn't that show.
I think, I really mixed my memories.
There was a girl in that cartoon, and dogs acted like dogs. They speaked, but they hadn't any clothes or anything.