Unemployment insurance is voluntary in Denmark. This means that you are not automatically insured against unemployment.
If you want to be insured against unemployment in Denmark, you have to take out unemployment insurance with an unemployment insurance fund (A-kasse). These are private organisations that are often linked to specific labour unions. You do not have to be a member of a particular labour union, however, to take out insurance with a particular unemployment insurance fund.
In order to receive unemployment benefits, you must
• have been a member of an unemployment fund for at least one year
• be able to take up work with one day’s notice (and have the right to reside and work in Denmark)
• have had a certain minimum income (in total) during the last 3 years (while being a member of an A-kasse).
You can find a list of unemployment insurance funds (in Danish) here.