High, High and Higher. You will certainly want to structure yourself correctly to avoid paying too much. With a top tax rate on earnings of over 60%, and "normal" rates of over 40% you'll wonder why you bothered in the first place. Here's the possible options as I understand them.
Employee You are simply an employee of the company as you would be in any other country. Your employer deducts your taxes and you get the net amount.
Enkeltsfirma You work for yourself and pay a corporation tax rate of 30%. When you pay yourself you just pay the difference between that and the personal tax rate. You can retain earnings within the company for distribution in future years and thus avoid the highest tax rates. One of the key rules for this criteria is that your business has to have at least 2 forms of income. Eg. two clients.
Aps or A/S These are the equivalents to Limited companies in the UK. Major difference being that you have to put up at least a hefty 125,000 krone minimum to capitalise your company whereas in the UK it's only £100...furthermore the tax advantages as far as I can see are more limited since your company has to pay corporation tax of 28% and you have to pay income tax, albeit at different rates, on any dividends you receive.
Branch of foreign Company If you have a British Company, for example, you can just open up a Danish branch, pay corporation tax of 25% and repatriate your profits back to the UK without any further taxes being payable even back in the UK. Could be a good option if you're only here a short while, but I have been told foreign branches attract closer scrutiny from the tax office and if you're a one-man company with no other earnings you should probably take advice.
Sponsorship of highly-paid workers If your pay is above a certain level (I think about £60,000) and you can find a Danish company to sponsor you, you can move here for up to 3 years. Then you have to leave, and you can't return for a very long time to live or work here again, unless you are willing to back-pay Danish taxes on all the money you earnt...sounds a bit xenophobic to me, and apparently in practice people commonly say it is hard to meet all the criteria of this rule anyway!
I personally went for the Enkeltsfirma, because I intend to live here for longer. I do accept however that the taxes are higher than the foreign branch option which I will investigate further if business develops well...and if business develops really well then I'm off.