It’s 112. In most places. From most phones. Most of the time.
Actually, it’s complicated. Right now the whole system is moving towards unification, and by 2017, you will be able to call 112 anywhere, from any phone, to report any kind of emergency.
But right now, the numbers to call depend on what phone service you are using. From a landline, call 01 or 101 for the fire department and emergency services; 02 or 102 for police; 03 or 103 for an ambulance; and 04 or 104 for a suspected gas leak. All the major mobile phone operators use 112 for all emergencies.
On MTS and Megafon, you can also call 010 (fire); 020 (police); 030 (ambulance); and 040 (gas).
On Beeline, call 001 (fire); 002; police; 003 (ambulance); and 004 (gas).
On Skylink, call 901 (fire); 902 (police); 903 (ambulance); and 904 (gas).
For information, call 009 from any phone provider. This is a paid service (66.05 rubles a minute) and only in Russian, but nice people will get you any phone number 24/7.
It’s also a good idea to know your embassy number. Because you just never know.