Of course that depends on many factors, such as the childs maturity level, their own comfort level, the neighbors, and your relationship with them, and how long you intend to be gone. A short trip to the market with a 10 yo at home is probably OK. An evening out on the town, I would want to have a neighbor or other responsible trustworthy adult on call, and would probably not leave any child under 12 alone for more than an hour. Leaving children of any age home alone has it's risks. You know your child. I would expect that if he/she can babysit, staying at home is no problem.
As far as at another child's home, that would be on a case by case basis, and only if I was very comfortable with the child's family. Again, any age can be trouble.