Due to the compact size and dense population, unlike the other Scandinavian countries, Danes and visitors does not enjoy the Right to access in Denmark, visitors who want to enjoy the outdoors can overnight in one of the more than 500 camping grounds, most are well equipped with up to date facilities. The Danish Camping Board (http://www.danskecampingp...) maintains a list of official camping grounds on their website. It is also possible to do wildlife camping in forests or other untouched sights, but only in designated areas there is about 800 of them. Unfortunately the digitalized information of the locations are in Danish only, but it can be found at the Danish Forest and Nature Agency (http://www.friluftskortet.dk/), another option to find these sights are to buy a printed guide book which costs DKK 98, and is available from many tourist informations desks or the Danish Cyclist Union (http://www.dcf.dk/)
For Budget accommodation, Danhostel (http://www.danhostel.dk) is the national accredited Hostelling International network, and operate 95 hotels throughout the country. Only the country's two largest cities - Copenhagen and Aarhus, have a few independent youth hostels. It is worth noting that the Danish word for hostel is Vandrerhjem, which also what hostels in Denmark are usually signposted as. Another option is one of the Hospitality exchange networks, which is enjoying growing popularity among the Danes, with couchsurfing reporting a doubling of available hosts every year.
Hotels are expensive in Denmark, with an average price of a double room hovering around 847 DKK $158/€113 in 2007, hotels are mostly off limits to shoestring travellers, although cheaper deals can most certainly be found, especially for online bookings done in good time before arriving. National budget hotel chains include Zleep (http://zleep.dk/) and Cabb-in (http://www.cabinn.com/). Alternatives to hotels include a well developed network of Bed & Breakfasts which are bookable through the national tourism organisation VisitDenmark (http://www.visitdenmark.com) Click on Accomodation > Private accomodation - or in country famous for its bacon, butter and cheese - what better way to dive into Danish culture than on a Farm Holliday? the National organisation (http://www.bondegaardsferie.dk) maintains an online catalogue of farms offering stays all over the country in both English and German. Another alternative to hotels are the many historic Old inn's - or Kro in Danish - dotting the towns and villages, most of them are organized though a national organisation called Danske Kroer og Hoteller (http://www.krohotel.dk).
Another option is to rent a private apartment when visiting Copenhagen which gives you the opportunity to stay in comfortable surroundings with facilities such as your own kitchen and Wi-Fi. The company Apartment in Copenhagen (http://www.apartmentincop...) offers 1-4 bedroom apartments at rates from 85 Euros per night.