European Parliamentary elections will be held in Denmark on Sunday, 25 May 2014 for the election of 13 members to the European Parliament.
If you are a European citizen living in Denmark you have the right to vote in the European Parliament Election in Denmark, if you registrered and vote in the European Parliament Elections in 2009, and have not moved away from Denmark since then you will still be registered to vote according to the information I found in the administrative act from 2009.
The information below is adapted from 2009 is from the EU information site of the Danish Parliament:
EU citizens who are residents of Denmark and who by or before the election day have reached 18 years of age are entitled to participate in the elections in Denmark as voters as well as candidates. However, persons who have been deprived of their legal capacity, cf. section 6 (legally incapacitated) of the Guardianship Act, are disqualified from participating in the elections.
(Of course) voting is allowed in one EU member state only No voter is allowed to cast his or her vote in the European Parliamentary elections in more than one EU member state. Your home country will be informed that you are enrolled in the electoral register in Denmark.
Enrolment in the electoral register before Monday, 21 April 2014 In order for you to exercise your voting right, you must first be enrolled in the electoral register via the relevant application form, which you fill out and forward it to the local national registration office in your residential municipality. The local national registration office must receive the application not later than 5 weeks ahead of election day, Monday, 21 April 2014. Already 3 months ahead of the election day, you can enroll in the election register.
After you have submitted your application for enrolment in the electoral register the local national registration office will inform you whether or not your application has been granted.
Not later than 5 days before election day will you receive a poll card indicating the specific polling station you will have to go to in order to vote on election day.
How to vote in Denmark 
Advance voting up to Friday, [23 May 2014] If you are prevented from going to the polling station on election day, you have the option of casting your vote in advance. In Denmark you may cast your vote in advance at any local national registration office or citizen service centre – i.e. not limited to the local national registration office or citizen service centre of your residential municipality – as from [Monday, 23 February 2014] up to and including [Friday, 23 May 2014].
Advance voting if you are staying abroad If you are staying abroad, you may cast your vote in advance at the local Danish embassy or consulate. Abroad you may cast your vote as from [Monday, 23 February 2014]. You must cast your vote well ahead of election day to ensure that it can be dispatched and received by the municipality that has your name recorded in its electoral register, before voting starts on the election day.
Evidence of identity When casting your vote in advance you must produce evidence of your identity (passport, driving licence or similar).