Even if not for property and belongings, I keep it for the liability.
The owner of my residence obviously has the property insured, which would cover things like someone slipping on the front walk or falling from the porch. If someone inside my house slips on a floormat that I placed, and breaks their leg...that could end up on me.
When I was younger, I kept renter's insurance purely for my belongings - namely electronics, computers, and bicycles. The policies covered bicycles lost by theft outside my residence, as long as they had been locked up.
I filed claims on my insurance for stolen bicycles twice over the years, and that alone made the cost of having the insurance policy worth it (was a big college town, bicycle thefts quite common).