Most Danes would say football is our national sport. It's the most played sport. Many, including myself, would probably say handball. It's said that handball was invented here in Denmark and many young people play this in the winter or if they don't want to play football. These are tier 1 sports in Denmark.
Gymnastics is widely exercised among children in Denmark. Children mostly learn skills and techniques from artistics gymnastics and combine it with music. It's not really rhythmic gymnastics, more like basic jumps from articstic gymnastics combined with music.
Swimming also has a big tradition in Denmark. Many children learn to swim from an early age and some continue on a more competitive level.
Badminton is the big racket sport in Denmark. Many great results from Danish badminton players has made thie sport popular. Tennis would probably be bigger if it wasn't for all the rain we get...
Denmark is a cycling nation, but few people is part of a club and pursue a professional career.
We have also incorporated many of the traditional sports from the British Empire back in the late 1800's and some are still widely exercised, like sailing and rowing. Cricket has disappeared, but we still have a national team.
A niche sport like speedway is relatively big in Denmark, but not on the same level as in Poland.
For winter sports, curling is probably considered our national winter sport. Though, most danes prefer to ski during the winter, either alpine or cross-country, when they are on vacation in Norway, Sweden or the Alps.
Some sports that are growing in Denmark are floorball, basketball, american football and ice hockey. The last three are due to more focus on NBA, NFL and NHL.