I have bought several things on Craigslist; a tiller, a tv, a pickup, 2 cars, a garden tractor, and several other things.
I am very mechanically inclined and have a pretty thorough checklist when looking at used equipment. When I was looking for a car a few years ago, I walked away from over a dozen cars because I found something wrong that the seller didn't tell about.
If you aren't mechanically inclined, and are looking for a push mower, you could ask the seller if you could mow a little in his yard. If it starts good, doesn't smoke when you start it, doesn't vibrate excessively, stays running well for at least ten minutes, and restarts easily immediately after shutting it off, it should serve you well.
If you are looking for a riding mower, there are a lot more things to look at.
What other things are you looking for?