You can take out insurance with any insurance company with registered offices in the European Union. The exact nature of the insurance cover you wish to obtain (abroad) makes no difference. This includes fire, life, car or personal liability insurance.
However, insurance providers abroad are entitled to refuse your application for insurance. It is up to them to define which risks they are prepared to cover, or not cover.
In reality many insurers refuse applications for insurance originating from abroad, often quoting the reason that the risk is situated outside national boundaries, which means that they would have to comply with countless national laws and licences.
ECC Belgium covers several important points on how to obtain insurance in Europe: