For some reason, I tend to agree with the others that say they would walk somewhere, but not get in a car. I don't know why I have that feeling though, since the chance of something happening in other case is small.
Honestly though, I would probably never leave my kids in the scenario you describe because I never run 10 minute errands. If I had to go to the ATM, I would go in conjunction with another trip (grocery store, whatever) or ask my husband to get money on the way home. Same with trips to the bank, post office, etc. I always combine trips because it just seems wasteful to me otherwise (not preaching, just stating my feelings). The only situation I could envision where I'd be gone literally 10 minute is to run something over to a next-door neighbor's house. In that case, sure, I'd leave the kids home, why not?