Well I have a clean and tidy house without behaving as Cattleprod suggests. Children can play, drop crumbs and eat chocolate in the living room, but it all gets tidied up at the end of the day and spillages get wiped up as they happen. My girls are 12, 7 and 4 so not babies but seem to make as much mess now as they ever did... I work part time which helps, and DH is away a lot which is a mixed blessing - less mess but no help!
Luckily our house has lots of built in wardrobes, 2 in DD3s room so all the toys are in one big deep cupboard and I have lots of those plastic boxes from The Range to fling stuff into and stack them in the cupboard. Bookshelves for books and a big tub for dressing up stuff.
The kids can go gonzo all day with toys/books/colouring/dressing up/whatever, but before bathtime have to help me tidy up. Whilst they're in the bath I might clean the shower/loo, or put washing away.
I declutter regularly and am fairly brutal about chucking/recycling stuff that is broken, pens that have dried out etc.
I clean upstairs when they're at school/nursery, and run through downstairs when they're in bed. I hoover downstairs daily (it only takes 10 minutes to do once they're in bed) and wipe/dust. The kitchen is done as I go along (a dishwasher helps, I fill it throughout the day and put it on as I go to bed) and I'm quite averse to clutter and knick-knacks so not too much to dust (just lots of books on shelves!)
I find that the more you can keep on top of it, the easier it is and the less time it takes. Having 3 kids, 1 who is disabled, and raising them alone a lot because DH is away, and working myself means I just have to be really organised or I'd go stark raving bonkers and none of us would ever have any clean clothes or toothpaste!
Lists are your friend
and never leave stuff out when it could be put away somewhere. Have a box or filing cabinet for paperwork and deal with it ASAP, clean the shower whilst your in it on a Saturday morning, do the ironing when kids are in bed (futile trying to do it when they're around) and empty school bags and lunchboxes as soon as they get in.
My girls certainly seem happy enough and are hardly confined to one toy at a time, they just know that at some point before bedtime they will be expected to help me clean it all up!