Step 1. The first thing you need to do is stop adding to the collection of JUNK that seems to end up
Step 2. Talk to your friends and relatives. Let them know that you are clearing things out. They might have some ways to help "make things disappear" or they will at least know that they don't need to add to the collection any time soon.
Step 3. Give them the opportunity to pick out what they want to lose first. You can get creative with this, too. You can put out some boxes with labels that show whether the child wants to sell it (garage sale! Let them keep the money!), donate it to children that don't have toys, or toys that are broken and need to hit the trash can. This can amazingly cut that pile in half.
Step 4. Pack up half of what's left in storage tubs. They can pick what goes in them to play with later, because it's time to rotate. If your child has too many options, they lose imaginative skills. They need to be creative with what they have! You can switch them out every six months, which gives you another opportunity to clean out the newest junk.
Step 5. This may be hard at first, but you can tell your child(ren) that if you find a neglected toy where it doesn't belong, it goes in a donation box. Basically, "It's mine. You lost it when you decided not to take care of it." It hurts at first, but eventually they'll catch on.
Step 6. If you really want to get creative about it, and if you are friends with moms that have kids near the same ages, you can put things into a trade box. Each kid has to put several toys in a box so they can choose one "used/new" toy out of a friend's box. This way, they may be losing a bunch of toys, but they get something else to play with. Take what's left to a facility that helps foster children!
Next thing you know, you have managed to get rid of at least a fourth of the junk that's taking up so much space. You won't hear "I"M BORED!" quite so often. The only project left will be to show your children how to keep what they have organized. Unfortunately, this is a "lead by example" situation. Have them help you organize a room that you've been ignoring, and in turn, help them organize. It won't happen overnight, that's for sure. But either decide to take action, or keep stepping on toys. Your choice!
NOW GET ORGANIZING!