This is available through a number of providers such as TDC and Cybercity via your telephone line and there is now also a company called ClearWire which is implementing a Wimax solution across Denmark. A lot of the larger towns are now covered, and this could be an interesting proposition since if you couple it with IP telephony like Skype
you'll have no need for a fixed line at all. Mobile phone provider 3 (Three)
recently
started offering Mobile phone internet with a speed up
to 1.5MB, which could also be of
interest.
A lot of garages and TDC sell mobile internet cards allowing you to connect to their local wireless networks for 1 or 2 hours at a time. This might be an option if you only need occasional access, although it is fairly expensive.
Now for something you really need to be aware of, the world's tax champions recently changed the rules so that anyone with an internet connection speed of over 256k has to buy a TV licence...which was renamed a "media licence", even if you don't actually have or ever watch TV. This new regulation has brought a lot of complaints from foreign students since Denmark also holds the distinction of the world's most expensive TV licence.