In terms of cyclability Denmark has a reputation similar to that of Holland; in fact the use of bicycles in Copenhagen is almost as prevalent as in Amsterdam, bike paths are widespread in the rest of the country, perhaps a bit less than in Holland but on the other hand are very well-signed.
In fact, Denmark was the first country to have introduced, in 1993, a unified system of bicycle route signage: signs are always of blue background with white lettering. Many carry a number that indicates the route which includes the following: if the number has a red background it means a national route (from 1 to 15), if it has a blue background it signifies a regional route (if two digits) or a local route (if three digits); signs without route numbers provide local directions only. The photo to the side is an example outside the city just south of Copenhagen. This is a good example for other countries to follow, from Italy to Germany to Austria where the signs are determined by local agencies and various organizations so that there is a true chaos of colors, shapes and numbering systems.
The prime difficulty that I found was in finding Danish biking maps; there is an excellent bike route map at 1:500,000 of all of Denmark, the Cykelkort Danmark published by Nordisk Korthandel. Hoping to find maps with greater detail, I was told to try the bookstores in the first towns I came to in Denmark (Rødby Havn, Maribo, Sakskøbing), but all I could find was the same map referenced above in a card shop in Sakskøbing. More than likely I could find maps at a larger scale in Copenhagen, but by then I wouldn’t need them anymore!
The primary Danish roads, both national and regional, almost always have at minimum a bike lane next to the road and often a true and dedicated bike path separated from the roadway. Even in Copenhagen many, many streets have a bike path located between the road and the sidewalk. These paths are quite wide and generally one-way, given that bike traffic can be quite intense.
I have found the urban cyclists in Copenhagen to be better disciplined than those in Germany or Italy; they always respect the direction of the bike path and use hand signals when they stop, but on the other hand they ride at higher speeds; therefore, foreign cyclists should be careful not to stop or slow down, as they might be knocked over by cyclists behind them; it's a good idea if you need to stop to follow the example of local cyclists and raise your hand so it is clearly visible.
A problem similar to that found in Holland is the presence (not frequent, but this has happened to me several times) of motorcycles on the bike paths, which are always marked with the classic blue round sign with the outline of a bicycle, a sign that, according to the rules of the road, should indicate a roadway reserved for bicycles and closed to motorized traffic. Apparently in Denmark the sign also includes motorcycles, or it is just an abuse that is tolerated? Certainly the problem has a fairly limited impact on the flow of bicyclists thanks primarily to the fortunately low number of motorcycles in comparison to bicycles. However, to me it seems a highly questionable acceptance that threatens to undermine the very concept of having a bike path; even just a moderate increase in the number of motorcycles would lead to the demise of bike paths as such.