
When I was in a MOPS group, one woman in my group was at her whit's end, trying to come up with a way to control the toy situation at her house. She asked for solutions and didn't really get any helpful feedback. It appears that everyone had the same problem and no one knew what to do about it.
Later that year I met my best friend, who happens to be the the most organizationally gifted woman I have ever met. She has great ideas. Her house isn't perfect, but that's just because she has little ones and a hubby. If she were single she would be "a fearsome sight to behold". I think that everything her shadow touched would miraculously alphabetize, sort, purge and compartmentalize.
She came up with a great solution for containing the flood of toys.
Start by sorting toys according to type: cars, Barbies, stuffed animals, Transformers, legos, balls, etc. Then put each pile into its own container (preferably clear, but opaque works too, you just have to label). The key is not to have much miscellaneous stuff left over. The SMALL pile of miscellaneous stuff goes into its own box.
Next, flex your muscles. Lug each of these boxes (reserving a few) to a closet, shelf, basement, attic--somewhere separate from where the kids will play or at least out of reach. I use Gem's closet shelf, a whole floor and dizzying height away from our play room.
Next, Lay down the ground rules:
1. Only one box open at a time
2. Only mom opens a box
3. Old box has to be put away before mom will open a new one (great motivator)
The key is training them. It's hard at first because they don't believe you. Their jaws drop to the floor and eyes pop from their sockets in horror and disbelief that their mother would expect them to play with one box at a time. They will even trespass rule number two. But after you deal with that a few times they begin to come out of denial and realize that playing with one box at a time is actually possible and (dare I say it) enjoyable. They no longer have to wade through a mass of other toys to get to what they want. It also allows them to focus their play and not get distracted.
I know of a mom who got so sick of the toy mess that she packed all of them up except two of her son's favorite matchbox cars. The boy played with those two cars for two weeks and when she offered him other options he declined.
Anyway, back to mechanics of how this works. I keep toys in reserve. I have about four boxes that I put high up on a shelf in the playroom (little kids can't reach and older ones better not even think about it). They are my main rotation. Every month or two we trade in for 4 new boxes from Gem's closet. This makes old toys new and keeps clutter to a minimum.
The boxes that reside in the playroom may be opened and played with one at a time.
Other stuff you'll run into:
Problem: You find three legos and an action figure gun that were hiding under the cushion on the day that you traded up for new boxes--which are now stowed under a stack of boxes a mile high in Gem's closet.
Solution: Just throw them in a small container labeled "restock later" and
keep it away from the kids. If you allow the miscellaneous stuff to pile up you'll have a sea of junk to wade through soon.
Problem: My boy doesn't want to play with the Barbies and my girl doesn't want to play with Transformers.
Solutions:
1. Allow two boxes to be opened.
2. Tell them that they have to agree on a box or no box will be opened
3. Suggest each child gets 30 min. then switch--set a timer so that they can't argue over time elapsed.
Problem: Large toys that don't fit into a box
Solution:
1. Stow them away as if they were a box.
2. Leave them out, without all the little pieces that go with it (kitchen set without the food and pan pieces)
3. Keep them with the box that they go with (see picture below)

That's about it. It works beautifully and makes clean-up a snap. You just have to keep tabs on it every once in a while. Mine still try to break rule #2 from time to time. Then I have a "boot camp" week of me being vigilant, and that's the end of that for another 6 months or so.
The initial investment, of work and purchasing containers, is a small price to pay for a relatively clean play area and a lot less hastle for you and your kids.