The problem with Skye, as Kathleen points out, is that more people are drawn there in recent years and despite increased accommodation there's never going to be enough to cope with the influx. I suspect just a few of the 'hot spots' on the island are overrun and the rest is pretty quiet as it always has been.
The Black Cuillin is the only alpine mountaineering equivalent in the UK and this will attract hardened climbers and walkers from all over, but because they are so strenuous and difficult they'll hardly be overrun. Not quite yet anyway.
And as also pointed out there are many other equally interesting places on the mainland. We went to the Outer Hebrides a couple of years back and climbed Clisham, the highest peak there and exited down a pathless glen. Didn't see a soul all day! And it was largely the same with the coast, beaches etc. It is possible to find solitude if that's what you are after. And equally beautiful solitude at that!