The short answer to this question is yes, cellphones can be used for emergency numbers such as 911 or 112 just like regular landlines. However, in some regions of the world including several US states, emergency services have established alternate emergency numbers which people with cellphones can also use, and you may want to familiarize yourself with regional emergency numbers before you travel. It is also important to remember to emergency numbers for their specific purpose; in other words, you should call the police to report a life-threatening traffic accident, but you should use a non-emergency dispatch number to report a theft.
Many nations have established universal emergency numbers which can be dialed to feed to local dispatchers. When a phone call to such a number is placed, the phone system routes it to the closest dispatcher, who routes requests for ambulances, fire trucks, police, and so forth. In addition to these universal numbers, it is also possible to call regional emergency services directly with their access numbers, and many regions have hotlines to call report things like environmental emergencies such as oil spills.
When you use a cellphone for emergency numbers, many countries have a law which states that you must be connected to emergency services, even if your cellphone service has lapsed. The phone grid pinpoints your location by looking at the cellphone tower closest to you, and routes your call to the emergency services dispatcher who is best equipped to handle it. In phones equipped with global positioning systems (GPS), your location may or may not pop up on the dispatcher's screen to help him or her find you when you use it for emergency numbers.
As when you use any phone for emergency numbers, you should be prepared to quickly and concisely explain the problem to the dispatcher. Also be aware that not all dispatching systems conveniently graph your location; be prepared to give directions, using available landmarks to help emergency responders orient themselves when they are looking for you. If you are traveling in a nation where the predominant language is not your own, make this as clear as you can to the dispatcher; he or she will find a translator, if possible, to help complete the call.
Typically, when you use cellphones for emergency numbers, you are not charged airtime. Remember to stay on the phone until the dispatcher has told you specifically that you can hang up, and follow his or her directions precisely, even if they may seem odd; dispatchers are trained to handle a wide range of situations and they speak from experience as well as their training manuals.