Personally I think a small air compressor is a pretty good addition to any car kit. Off the top of my head, I can think of several uses for a compressor in a passenger car:

You go to change a tire just to find out your spare has deflated over time (I've seen this happen on a few occasions) the air compressor can re-inflate the spare and your good to go.

If you don't have a spare, or you cann't remove it from its carrier, you can inflate your flat tire and limp to a service station. I saw this happen on a truck once, the owner had installed a tow hitch that interfered with the tire carrier making it impossible to remove the spare tire.

In low traction situations like snow or mud it can be very adventageous to air down your tires for added traction. Of course you wouldn't want to drive like that on dry pavement, so you'd use the compressor to air your tires back up. I do this all the time when I go Jeep'n, and I've even done it on a few of my friends's cars, and it works great.

Once I was traveling through the snow with my friend in his rear wheel drive volvo station wagon. The back was pretty loaded down, so when we went to put the tire chains on, we didn't have enough room between the fender and the tire to fit our hands to install the chains. luckily he had a small compressor with him, so we deflated his tires, installed the chains, and then partially re-inflated his tires. Worked like a charm.