Had me tickled too!
We have toys sorted by type - cars, playmobil, dressing up, construction, pretend play etc in some boxes in the bottom of our storage cabinet, freely available. I do ask that if one comes out, another goes away, and it seems to work. We also have some other stuff like games and craft supplies tucked away in the cupboards and a craft area permanently set out ready to go. With the organiser I bought just before xmas the craft stuff can all be out but also tidy - and that's what gets the most regular use in our house.