Despite the wide range of variations, there is a method in the madness. Most countries started to implement their telephone infrastructure in the early years of the 20th century, at which time DTMF tone-dialling was unthought-of. All telephones worked on the pulse system, whereby dialling a number would make and break a circuit to cause a series of electrical pulses to travel down the wire.

When the emergency number systems were first thought up, there were two main criteria:

(a) The number(s) had to be easy to memorise, and
(b) They should be easy to dial in the dark or when surrounded by smoke or whatever.

Working on this principle, the first suggestion was "111" -- about as memorable as anything else could be, and easy to dial even if you couldn't see what you were doing, as "1" (on an old-fashioned rotary dial phone) is just one finger hole away from the zero which was always at the bottom of the dial. Zero itself could not be used as it was used to get through to the operator at the local telephone exchange switchboard (this was long before direct trunk dialling came along).

However it was found that the wind blowing through telephone cable suspended from poles out in the street could sometimes cause a fake pulse to travel down the wire; it didn't take long before they realised that having the weather call the police or fire brigade was probably not a good thing. Another number had to be chosen: in the US they simply substituted the first "1" with "9" -- 911 -- in the UK they replaced all the "1"s with "9"s -- 999 -- and in other countries other similar ideas were used. The Americans apparently investigated the British 999 idea but rejected it as on a pulse-dialled phone, a "9" takes nine times as long to go through as a "1" does. 911 was chosen as the fastest, easily memorable number which didn't cause a host of fake calls.

Many thanks to my grandma who spent all her working life as a telephone operator and filled my head with all this trivia.