Just saw a bit on MSN about a guy who got busted for buckling up his beer instead of his toddler.
Recently, I seatbelted two bougainvillea potted plants to keep them from falling on the floor on the drive home from the horticulture sale.
Have you ever put a seatbelt on a pet, object, six pack, or something else that wasn’t a human passenger?
I put a seatbelt on the cake container which I am often carrying to morning teas at work.
Computer monitors are a big one. Anything fragile, really. Who wouldn’t?
I always belt my cats (while they are in their carriers ) in very securely on trips to the vet.
I’ve put seat-belts on computer towers, monitors, and TVs before.
I don’t know why you’d want to seat-belt a carton of beer, though- they fit quite comfortably in the footwell behind the seats and won’t move around there. 
TV
Vases of fresh-cut flowers
Dog
Yes: alcohol.
This last Christmas, I was nearly done with my shopping and needed only to get wine for the holidays, for gifts, meals, and general drinking. At the wine store, I ended up with a case plus a few, so the nice gentleman put it in a box and carried it to my car for me.
The trunk was already full with gifts, so he put it in the passenger seat. As I pulled away from the curb, the seat belt warning dinged again. My car apparently has sensors in the seat, and because there was weight in the passenger seat, the car assumed that there was a person there that ought to belt up.
I finally pulled over, belted in the wine so the dinging would stop, and continued home.
All the time. I usually have to transport trophies after debate tournaments, and some of them can get rather large. So they get strapped in the passenger seat of my truck rather than wedged behind the seats.
I used to have a handy storage container – like in a nice car’s armrest – in the center of the bench seat of my truck. That sucker would have slid off at every stop sign if it wasn’t buckled in. I finally got rid of it because it was too much hassle to mess with it all the time – I could open it with the belt on, but then it was difficult to close.
I gave it to a friend, who has it buckled into the center of the bench seat in his pickup.
When I moved to Wisconsin (then back to Kansas) I belted in my computer, my monitor and we also belted in a TV in a different car.
I knew someone who bought an extra seat on a plane and belted in a very large vase from his archaeology dig. 
Wine bottles. I have no idea whether it would do any good in the event of a collision.
I’ve belted grocery bags (worked best for paperbags, not plastic).
Ditto that.
Beagle
Of course. Anything that would be harmed or broken if we stopped short. Computers, glassware, my dog (in his harness), etc.
Besides pet carriers and computers? Dorm refrigerator. It’s heavy and you don’t want it to jump forward and slam into the front seat if you need to hit the brakes.
I don’t have a cite for it, but a few days ago in the local paper, there was a story about an a man in Australia who got popped by the cops for putting a seatbelt around the case of beer he just bought while leaving his infant son unrestrained.
Once my sister and I went grocery shopping and picked up a large watermelon.
When we got back to our car, we put in on the backseat.
Then we decided it looked like a child, so we buckled it up.
It was quite cute really
I’ve done that with a Betacam when I was using a vehicle other than my usual one and in a huge hurry with no time to load a case.
I believe that’s the incident the OP is referring to.