Fake responses to my Craiglist ads, offering to have shipper come to my house and send me cashier's check or Paypal.  Clearly fraud is the goal.

Same here. Stay clear.

Craig's List wants to pay by PayPal. Buying item site unseen and states he works at the AIr Force base in Ohio.

The person's texts to me:

Hello, what is the lowest you'd go for the  2008 Suzuki SV650 ABS $3,800 - $3800
?
Alright id buy it for $3600 as long as nothing is wrong with it and the description is accurate.Are you the first owner?

Indeed..sounds good,am satisfied with the condition.. I'm just trying to make sure its in good condition because am buying this for my  lovely son as a birthday surprise gift, which i don't want him to know about. Whats your reason for selling it?
Ill be paying instantly through PayPal because I'm at the Wright-Patterson Air Force Base in Ohio. I have a Mover that will come for pickup once payment is cleared in your PayPal account

I told them "no" and have ignored them since.

Same thing with me.  Someone fishing on my Craigslist ad for a motorcycle. Told them I only sell local.