Ditto what Rio said about low traction situations. Most "all-season" tires are in fact 3-season tires. But drop the tire pressure to about 17 lbs, and drive slower, and you have a lot of extra 'grab'. Did this a lot when I was younger and poorer. Now that I'm a bit older and a bit less poor, I buy first-class ice/snow tires on separate rims; worth every penny, never looked back. But then there's the rental car scenario, in that sudden ice storm, and if you wish to stay alive ...

I often tuck a 12VDC compressor into a vehicle on a road trip. Especially older, more temperamental vehicles. Inflates tires, spares, and air mattresses (with electrical tape and a Bic pen adapter). When I forget to pack the compressor, I feel a bit naked; you can't improvise an item like this.

That said, with my everyday commute vehicles, I have one of those "inflate and seal" cans in the trunk. When you're half an hour from home, and wearing dress duds from a meeting, that $5 can of goo seems like the easy choice.