Always be aware of your surroundings. Avoid people coming up to you wanting your attention. Research where your lodging is located to make sure it and the surrounding area is safe. Protect your valuables.  Keep things of value such as wallets, phones etc out site as much as possible. Take precautions where ever you are and where ever you are going — to the trained pickpocket you look like a tourist, act like a tourist and sound like a tourist.

Who do I call if I need the police or an ambulance?

Throughout Europe you can reach emergency services by dialing 112 and 999 in the UK (it operates similar to 911). The major difference when calling for an ambulance is that in Europe the technician on the line will be a much higher trained medical person who will determine if they can solve your medical issue over the phone.  If not, they will probably send a doctor or other highly trained personnel along with an ambulance.

Dialing 112 should allow the emergency services to know your location via GPS. Also, you should be able  use the SOS Emergency calling feature to reach help even if you have no international calling plan.

Also, the local embassy website can be a great resource for information on local safety.