Hi Ilkka,
For private health insurance, the most popular private health insurance providers are:
Sanitas
Adeslas
Asisa
DKV
Assa
You can often request a quote on their respective websites or speak to someone on the phone to discuss the right plan for you. Coverage will depend on the plan you select.
I am from the US and reside in Spain and I have a private plan with Sanitas.
If you have any questions just let me know.
Cepee Tabibian, IL Correspondent - Spain