Clean Up, Clean Up, Everybody Everywhere....

So, how do you get kids to clean up their own toys?

I keep finding that we get to the end of the day and toys are everywhere and there's no time left for clean-up because they're late for bed already and/or misbehaving/falling apart emotionally from exhaustion and so they just get hustled upstairs and I either clean up the toys for them once the downstairs is empty and quiet or just trip over the mess exhaustedly and head up to bed myself. Terribly helpful, right?

I realize that its important to teach children neatness as a habit and I also don't want my boys to grow too entitled about their right to a mommy-maid or their right to leave every little thing heaped in piles on the living room carpet just...because. So, short of singing the Barney "clean up song" a lot in a cheesy voice, what do people do to accomplish this goal?

I've considered having a designated clean-up time before dinner but I'm not sure how to adequately supervise while cooking and if I do it before I start cooking, how do I keep the small people occupied while I am in the kitchen? Do tell how you organized mommy types have solved this dilemma, how you've seen clever mommies teach this lesson, great ideas you've read somewhere on the topic or even your own idealistic or wacky brainstorms to get the point across. I take all suggestions...really, I got nothing right now.