What is the emergency phone number in different countries?

You can find the list of phones in the Wikipedia: Emergency_telephone_number

For most countries in Europe is 112

This answer was posted in 2012, it is out of date now. Also in Belgium 112 has been the official emergency number for years now.

(In Belgium the number is suppose to be 112. Recently there was actually a message in the newspaper that you better not call this number yet. The Belgian emergency services can't come to an agreement how to manage such a number. As the newspaper quotes an official, the Belgian government instated 112 to communicatie to foreigners, but locals are advised to call the old emergency numbers (101 for the police and 100 for other services). Currently you can call 112, but you might be caught in an queue losing precious time.

I guess this might apply to other countries as well. So if you really want to know the emergency numbers of a country, the Wikipedia article mentioned by @SERPRO is a good starting point, but you might prefer the numbers mentioned in the Notes.

If you have an iPhone, I believe you can make an emergency call from the lock screen without needing to know a number.

Some other phones may also have a similar feature, though I wasn't able to find one on my Android phone.