My personal best was 37 minutes before I finally let the guy know I was stringing him along. I was working at home and had a whole lot of completely mind numbing tasks when the guy called so I could continue to work and mess with the guy.
I acted all concerned and said, let me get to my computer room, it is on the other side of the house and put the phone down for 2 minutes. Then I picked up he was still there so I said, hold on, it is booting...which one, I have 4? I told him, they are old and slow and will take a bit to boot hold on, another 2 minutes of putting the phone down.
Then I started playing along, acting like the horrible end user who is totally illiterate and can barely use a computer. Had "monitor issues" because it was unplugged. Didn't know where anything was. He told me to open a command prompt and type things in, which always resulted in Unknown command because i was "misspelling" what he told me because I was bad at typing or thought it was a different letter because of his accent.. He then switched to Alpha, Sam, Sam, designation and I pretended to type in alpha, sam, sam.
Then I used the bathroom, picked up stuff around the house a bit and finally needed to get back to actual work and told him, I will level with you, I do PC security stuff for a living, I have been messing with you the entire time.
He said, well this entire time I have been hacking into your machine and stealing all of your files and if you don't pay me, I will not let you have them back. I laughed and said, no you aren't to which he said, never underestimate the power of the common man. I told him, you are a common criminal and not that good of one and that lead to the tirade of swearing and he hung up!