In a recent interview with web site AllThingsD, chief executive officer of Intel Paul Otellini not only said that they (intel) would see off ARM, but also compared them to companies like Transmeta and Via. Transmeta designed ULP x86 compatible chips until they went bankrupt, Via made low power/cost chips but didn't get a foothold in the market.
He went on to say that the Intel range of CPUs are the best, are getting quicker than everything else and that they should also see off the ARM threat. Big words, but he certainly has the muscle in his products to back these claims up. There really is little out there to give Intel a run for their money. AMD aren't flush for cash at the moment and ARM are pretty much doing their own thing.
“People come and go, and we have never had an exclusive, if you will. And, overall, the best chip has won,” - Mr. Otellini.
It's a tough market and one that has undergone a lot of stress this last few years due to a drop in sales of computers and of course their components. ARM have some interesting solutions at the moment and with Windows being built to start running on ARM devices it's certainly gaining traction. Is Intel wrong to shrug them off so lightly? maybe not, but I think Intel's market share is safe, for now.