112 and 911 (US) work on almost every mobile phone anywhere in the world. It's part of the GSM/UMTS standard. 999 is supported with either no SIM card or a UK SIM card. See §7.1 here: https://www.ietf.org/lib/dt/documents/LIAISON/file562.pdf

They also don't require a phone to be activated in most countries. I believe there are some exceptions in EU countries, but in the US it just needs to have a working antenna and be in range of a tower.