As ever, coming from the EU or EEA offers an immediate benefit in terms of health insurance compared to most other countries. As long as you have a valid Eueropean Health Insurance Card (EHIC), you will be entitled to full medical care at the same cost as Swedes, but not more. If you’re staying for longer than one year (i.e. completing your full degree programme here) then you should register with the Swedish Tax Agency to get full entitlement to all Swedish healthcare.
You will not be able to obtain a personal identity number and therefore will probably not qualify automatically for health insurance. However, if your home country is one with which Sweden maintains a reciprocal agreement (check the list by contacting the Swedish Social Insurance Agency) then you should be okay.
Otherwise, it is strongly recommended that you obtain some form of private insurance to cover your stay, as medical procedures are very expensive in Sweden. It’s also possible that your university will offer you health insurance, so be sure to contact them before you leave to find out exactly where you stand.
Just like EU/EEA students, you can register with the Swedish Tax Agency to obtain all the medical and healthcare rights of a Swedish National, and pay the same fees. This will not cover your journey to Sweden, or the time spent waiting on your personal identity number (required to claim your healthcare rights) which can take a few weeks. To be absolutely covered, you should invest in short-term insurance to cover this period.
If you require an ambulance, fire engine or the police, dial 112. This is only for true emergencies, and any other problems should be reported to your local healthcare provider or hospital.