This delightful country, relatively unknown as a hiking destination, is a collection of large and small islands (that is, if you consider Jutland to be an island). The sea is omnipresent, as is a rural atmosphere, with plenty of sights and historical peculiarities. After all the Danish are a people who just as easily sailed the wild seas to Greenland, as they milked their cows. So, you will not get bored easily.
The different islands mostly offer coastal paths as well as trails into the interior. Beaches and dunes alternate with skerry and cliff coasts. European long distance trails E1, E6 and North Sea Trail all pass through Denmark.
Walking in Denmark requires something of a searching attitude. Many trails are maintained by local communities and tourist offices. Some trails are better documented than others, but generally excellent maps are available, and for free. Danish are fond of making leaflets. So, maps are often published specifically for hiking trails, showing special features and combined into handy brochures. They are usually available for free, and most of the time can also be found on the Internet. In addition there are various websites giving detailed information on trails, also in English.
In many cases hiking and biking trails coincide, so take care not to bump into one another. Along the way there are accommodations of all sorts, such as hostels, youth hostels and trekkers campsites. Trails are well marked. All trails are easily reached by train or public bus.