As I've already noted in REST vs. SOAP/WSDL, Amazon claims (according to Tim O'Reilly) that its AWS traffic is 85% REST, 15% SOAP. So REST proponents claim anecdotal evidence like this means REST is more popular.
They may be right--if SOAP and REST went up against each other in the People's Choice Awards (or their technical equivalent, the JDJ Reader's Choice Awards
But I'm interested in the enterprise application market, not the hobbyist market, and enterprise applications that use Web services use SOAP. I consult with customers using IBM J2EE products (WAS, RAD, etc.), and they're using SOAP. JAX-RPC, support for SOAP over HTTP and WSDL Web services, is part of J2EE. J2EE doesn't have any support for REST, unless you count servlets (which is kind of all you need for REST).
So the logic is kind of circular--J2EE supports SOAP, not REST; so that's what J2EE apps use--but nevertheless, that's how I see enterprise applications implementing Web services these days. SOAP is the established standard, REST is the opponent fighting SOAP for mindshare and trying to gain supremacy. Maybe it will; we'll see.
But for now at least, SOAP is the "most common" Web services technology.