320-245-0135 called and told me that they were from Microsoft and that there was a problem with my computer. They wanted me to turn on my computer and allow them to connect to it. The area code was the same as mine (Central Minnesota) and thought that this was fishy in itself since I know of no Microsoft offices in my area. I hung up on the caller.
After originally posting this, I searched for microsoft call scams and actually found Wired UK article that claims that this is a common scam. See http://www.wired.co.uk/news/archive/2013-04/11/malwarebytes for more detail. I didn't mention it at first, but the caller sounded like he was from India which is where the Wired article says this is being run from.
Got two calls from (320) 245-0135 today. Caller ID reports as coming from "Gafkjen Sherney". I never answer calls from unknown or unrecognized parties so I can't give any more details except that unlike Michael B. I live in Virginia, so this isn't limited to Minnesota.