Denmark's census is similar to those from other parts of the world, in a few ways. The first Danish census with the most relevant information for genealogical research is from the year 1787. It was taken again in 1801 and then there is a gap until 1834. There is also census information for 1840, 1845, 1850, 1855, 1860, 1870, 1880, 1885, 1890, 1901, 1906, 1911, 1916, and 1921. The last one available to the public is the 1921 census.
As with many censuses in the world, the first ones were not as informational as those in the later period. They did, however, contain more information than what is found in very early American censuses. Those from 1787 and 1801 included the residence, family number, the names of all people residing at that place, whether the children were legitimate or illegitimate, if they were from that marriage or another one, ages, marital status and if it was the parents' first marriage, and occupation.
The Danish census did change over the years to give more information. In 1834, the first taken after a period of 33 years, the census added the relationship of each person. Relationship was not always given to the head of the household. In addition to the main family, many homes included servants, and if these servants had children in the same home, their relationship would be given in regards to their own parents and not necessarily in reference to the head of the house. A couple of things were taken out in 1834 census, too. These included legitimacy of children and which marriage each of the parents was in.
The 1840 census form remained the same as the 1834, but in 1845 they added the birthplace of each person. The place given was the parish name.
Beginning in 1850 you can find the religion of your family. The reason religion was not added until 1850 was because up until 1849, the Danes were not allowed to profess any allegiance except to the state's Lutheran beliefs. A law in 1849 changed that and allowed for freedom of worship, so in 1850 religion was added to the census. The census information did not really change after the 1850 census was taken.
The Danish census can be accessed on microfilm from Denmark's State Archives in Denmark or through the Family History Library and any of its branch family history centers located around the world. When searching the Family History Library Catalog for the film number, you will find the censuses on the county level. If you would rather search at home using the Internet, you can do that, too. Denmark's Digital Data Archives were put online in 1998 and they are constantly adding transcribed census data to their collection. The site for that is www.dda.dk. They do not have everything completed yet for all the counties, so before you get discouraged at not finding anything, there is a place on the site where you can search to see what they do have online. You can use the site in English, or if you would like to test your Danish skills, you can also change it to Danish.
Because names were usually spelled phonetically, you will want to remember to pay attention to the tips on the right side of the search screen in the colored boxes. Those will make it easier to search than having to run a search for each variation.
I have found the Danish census necessary in all research I do in Denmark. Hopefully this overview will give you a jumpstart when you begin your search of this valuable record.