Extra Clothes, Paper Towel
What happens if you spill a drink, got splashed by a car driving by?
Gas Can
If you run out of gas, what are you going to do? You walk to a gas station, you are going to need a container to carry the gas. You will probably need one for your law mower anyway. Why not keeping it in your trunk?
Duct Tape
Duct taps can provide easy temporary fixes for some small problems, for example, if you mirrors got knocked loose. I once had to borrow some rubber bands from gas stations.
Shovel
This is useful if you get stuck in the mud or snow. You can dig your way out of it.