Hedra's amazing system of toy organization is so…so…amazing, it's a wonder we don't all do this.
To contend with the overflow of toys, without violating the principle of ownership (that is, the toys belong to them, not us), we instituted a toy library.
In the basement, we have a bunch of shelving units (Sears, plastic utility shelves), on which are large rubbermaid bins. The bins are labeled with things like 'dressup' and 'vehicles'. This is the toy library.
Children may check toys out of the library in any quantity at any time, provided they check an equal number of toys back in at that time. You don't even get to go into the toy library unless you have a toy or two (or six) in your hands, to turn in (No promising to turn something in later, it is too much to ask them to remember). Even the 2-year olds are starting to grasp this idea.
Additional functions of the toy library:
Toy timeout home. When toys are left on the floor after cleanup time, they go to the library for time out. That is, they get left in the timeout box until such time as I can sort them back into their appropriate bins. That technically is supposed to be a week. It functionally is longer than that. If you want a toy to remain available, it has to be put away. If they cannot or don't wish to clean up every little thing, that just means there's too much out in the first place, or the toy has lost its joy for the moment. No biggie. Toy timeout helps prune that down to a level that they can manage, and removes the less popular items from circulation (and from underfoot). That the toys aren't destroyed/thrown out/given away takes the fear out of the process, lets them retain ownership, but keeps me from suffering. Win-win!
Filter for toys parents dislike/disapprove of. Some things end up in the toy library more often than others. And some toys end up at the bottom of the toy library bin, under a bunch of other things that we prefer they play with. There's ownership, but there's also some sneakiness in parenting. Hmm, where IS that annoying toy that beeps? Must be in the toy library! Go look. Oh, look, you found something
more interesting than that (higher up in the bin). That's cool.
Reminder for relatives that buying more 'stuff' is not helpful. Especially if you get them to help you either make the shelves or sort things into the bins when they visit.
Easier to sort from for donations, garage sales, etc. This is still at the kids' discretion, since they own the toys, but seeing that they have two bins full of stuffed toys they aren't playing with may make it easier to donate a few to the kids in Iraq.
Enchances creative play through effective employment of laziness. You could pretend the stick you found in the yard is a sword, or you could go find a toy to bring down to the toy library, fish through the weapons box for the right sword, and then bring it outside. Sticks win far more often than I'd expected. As does swinging on the swings, climbing the boulder, and playing pirate on the playset.
Caveat: No matter how much everyone understands the rules, and swears they're following the rules, there is still 'toy creep'. More ends up in the living room than started there a week or two earlier. However, this is still vastly less than otherwise, AND it is simple to just pick up a load of stuff that is not in active use, and take it back to the library. No panic and pleading from the kids, once they understand they can get it out again if they need it.