We have a little round footstool that all the tiny stuffed animals can go in. The big ones are one the ends of the beds, and a few are on top of the tallest bookshelf, which reaches almost to the ceiling.
They have these 9 cube wooden shelving units (I bought ours at Target) that you can use both for open storage or use with the fancy canvas bins that come in a variety of colors and designs. I LOVE these for toys, because I can keep sets together and dust free.
We used to have an open bin shelving unit (the kind with the horizontal metal bars and the open plastic bins) and I HATED it. Nothing fit in them properly, and everything got dusty and I constantly had to clean toys.
For larger sets, I use Rubbermaid totes and store them in the basement. Every time my children want to play with dinosaurs, or Barbies, or the train set, or the Pet Shop stuff, I have to trudge downstairs and haul up a big tote...but worth it to keep the stuff out of the way and then they have more fun with it anyhow.
Lots of shoeboxes under the beds to store other sets that don't get played with as frequently but haven't been banished to the basement.
I am also a fan of rattan baskets with nice linen liners. :)