The "non-emergency" number is designated to be "311" in the NANP. Some towns have this implemented (San Jose, California is one). There are other "N11" numbers in use as well.
311 Non-emergency police, etc. (as mentioned)
511 Traffic (at least in the San Frnacisco Bay area)
611 Repair. This is very system specific. Try to use your cell phone to get repair on your land line is a bit difficult.
711 Unknown to me
811 At times has been the "Business office". This changes quite a bit and is locally very different.
911 Emergency (usually life threatining). Expect someone at your door (ready to bash it in if necessary) very soon.
It used to happen that some "portable" phones would dial things as their batteries wore out. Typically "dial pulse" (make-break) style dialing. Sometimes it could do 911 which caused ALL sorts of things. Other times (it has been documented) that a dog got tangled up in a phone cord of one of those phones that had nice big buttons to dial an emergency number. Of course in the tangling up of the cords, the dog got the phone to dial the police. They came to an empty house and recued the dog. Wonderful story re-created for a TV show. Operator: "what is your emergency", Dog "Bark Bark...".