Sweden is an incredibly safe country. Serious crimes are rare, but that being said, crimes do occur. In 2014, according to The Swedish National Council for Crime Prevention (Brottsförebyggande rådet—Brå), there were 20,300 reported sex-related crimes, of which 6,700 were rape. Eighty-seven people died as a result of murder or manslaughter and 6,269 hate crimes were reported. And then there’s the pickpocketing—53,355 cases were reported. So yes, crime happens in Sweden. Serious crime, deplorable crime. With that in mind, it can be good to know some vocabulary that can help you in an emergency situation, whether it’s due to crime or just an accident.

Let’s start with the basics. Help. Hjälp. There’s the noun form, which can be useful to know:
Jag behöver hjälp. = I need help.
Jag behöver din hjälp. I need your help

Then there’s the verb form: att hjälpa
Kan du hjälpa mig? = Can you help me?

If you’re traveling, you may not have your phone with you, but you need to call the emergency telephone number, nödnummer in Swedish, which is 1-1-2. Do not call 9-1-1. It won’t help you much. You’ll need to ask to borrow a phone:
Kan jag få låna din telefon? / Får jag låna din telefon? = Can I borrow your telephone?
Kan jag få låna din mobil? / Får jag låna din mobil? = Can I borrow your cellphone?

Maybe you need to tell someone to call the police.
Ring polisen. = Call the police.

The police could come in handy if you’ve been pickpocketed:
Någon har stulit min plånbok. = Someone has stolen my wallet.
Någon har stulit min handväska. = Someone has stolen my purse. 

Or maybe you need to tell someone to call an ambulance.
Ring (en) ambulans. = Call an ambulance.

This is especially useful if there’s been an accident:
Det har hänt en olycka. = There’s been an accident.
Jag behöver en läkare. = I need a doctor.

Of course there are plenty of other situations where you might need emergency vocabulary (Det brinner. = There’s a fire. For example), but the above should give you a few of the basic phrases you might need. Hopefully you won’t have to use this new vocabulary, but it can be good to know.