I've had rubber chippings down in my run for nearly 3 years now. Initially, you cover the earth floor with permeable landscaping fabric, the kind used for weed control, in wide widths, and peg it down well round the edges. Then just pour on the rubber chippings, which are made of minced-up old car tyres, so good recycling. Instant transformation, no more mud, ever!! Once a week, or whenever you think it's necessary, you just hose down the chippings, dissolving the droppings, and water the run with a canful or two of suitable disinfectant, eg Barrier X or Poultry Shield. I use 100ml. to a 2-gallon watering can. The chips are always soft and warm to the chickens' feet, even on frosty days in winter, and their feet always stay dry and don't get muddy, because the membrane underneath prevents them from digging into the earth, although they can and do spend time scratching up the chippings to see what they can find. A handful of grain in the afternoons keeps them happy for a long time! The chips are nice and warm and comfortable and the birds often like to lie around on them for little naps.
My run is partly covered, partly open, so there's a dry end and a part that gets very wet in winter. Because the chips are non-absorbent, they never get soggy and drain and dry off quickly, so are always pleasant to walk on. You do need well-drained soil under the membrane, so the hosing water can drain away adequately, (probably not so successful on slabs, for instance) but given this, the chips do solve the mud problem, as the birds can't get at the earth but instead walk around all the time on about 4 inches of rubber chippings. They are more expensive initially than other surfaces such as woodchip etc, but if correctly maintained will last for ever and never need digging out, disposing of and replacing, saving both money and effort in the long run. I like the way I can always keep the run fresh and sweet-smelling, not have to wait until it's really nasty before undertaking the horrible job of digging out filthy muddy flooring.
Downsides? Not quite so easy to poo pick as a soft disposable surface, because the droppings tend to stick to the chippings, which you don't want on the compost heap. I wear rubber gloves and pick up the intact ones carefully, and the soft runny poos I put in a bucket, with the chippings which come up with the poo, and when I've got half a bucket full I just hose it down, sieve out the chips, pour the fertiliser water on the garden or compost heap, and replace the cleaned chips in the run.. When installing the membrane below the chips, you need to be very careful to allow a good big turning under the cut ends, or preferably even measure, cut, and hem the edges on a sewing machine before putting it down, to avoid the birds pecking loose the frayed ends from the edges of the membrane. Apart from that, I think they're excellent and I wouldn't change now I've got them
(EDIT; 2018; On re-reading this thread, I want to say that eventually I got really fed up with removing and washing the pooey rubber chippings. they got into a state because over time the residue in the droppings became a solid layer underneath the chippings making it impossible to hose them properly. I bagged therm all up, took them to the dump, cleaned up the membrane underneath and substituted Aubiose, which I've used ever since. not only is it really easy to poo pick but it makes excellent compost, is very absorbent, and also the pale colour makes the run much lighter.,