I just got a call from this number claiming to be "Calltech" and saying that multiple computers have been added to my home computer network, and that they are hackers from a list of places, I think that Russia and Syria were among those he listed.  He said he got my phone number from when I purchased my (Windows) computer.  I have not purchased a Windows computer since, well, actually, I guess the last time was with Windows 2.1 back in 1990?  And I certainly did not have a cell phone back then!  The caller had a distinct (non-US) accent.

Just like Matthew says. Call from "Call Tech Support" (who claim to be Microsoft contractors, which is how they got my number), 5 computers, from Nigeria and Syria, etc. - the exact same thing. It was obviously a foreign call and the guy was foreign also (sounded East Indian). He said he had to get to work on my computer immediately. Being suspicious, I put the guy off. So I never did get to the part where they ask for money - but I'm sure it was coming. Here's the thing though, I actually did have a couple of suspicious incidents and my computer actually is running more slowly.

Same experience as above.  Asked if he had checked 'do not call listing'  -- refused to acknowledge question.  Claimed a hacker had infiltrated my computer and that he had sent me 'numerous' warning messages. I got rather erate and began asking questions how he had any info on me ??  Claimed he is a 'certified MS' vendor.  I suspect he is likely a hacker who is seeking to access my computer under false pretenses and then either steal info or sell some protective software.  Far eastern accent and very aggressive with his sales pitch.

Addendum ---  Caller ID identified caller as 'Kashif Ali'

My experience is the same as all the other folks that posted. "Frank" claims that at 9:45PM the evening of Oct 8, 2015 5 unauthorized computers accessed my computer. Fellow has a distinct Indian accent and is likely the same guy called the day before. 9 months ago they were calling on my cell phone. Tells me the event was going on all night and still going on. This is a scam to gain access to your computer under the guise of fixing the problem. Thing is, whenever I turn off my computer, I disconnect the Internet access cables so this can't possibly happen. It's something I recommend to every computer user to do, because there are hackers that utilize networks of computers for illicit purposes, including accessing your data. Once a back door is established to access your system, it is nearly impossible to uncover. I asked for a phone number to call him back and a case reference number and the connection started to break up. Funny how that happens. The 631 area code is Suffolk County, NY. The phone number he began to give was a Kentucky area code. Do not give these people any information or access to your equipment. You will certainly regret it if you do. It is a SCAM.