ICANN's application system for new gTLDs (TAS) closed to new registrants yesterday (March 29) as planned. The total number of registrants on the system isn't known yet, but ICANN has indicated that there were 839 registered TAS users on March 25.
In the run-up to the April 12 cut-off date for the first new gTLD application window there's been a real surge of TAS registrations. Each registered user can submit up to 49 TLD applications, so the latest numbers put the total potential number of new gTLDs that could come out of this first round at 41,111!
Final TAS user numbers should be higher than the 839 figure and could in fact be close to a thousand. It's clear that most users will never get anywhere near applying for the total number of TLDs their TAS slot would entitle them to, but some will definitely apply for more than one.
So total number of TLDs applied for? My guess at this stage would have to be somewhere in the region of 1,500.