I've recently started freelancing full time, and sometimes I need to employ other people on a freelance basis to help, either when the workload is too high or when I can't do something. Those freelancers give me an invoice which I pay. Can I deduct their fee from my income when calculating my tax return?
In Denmark, it would be considered a business expense which lowers your company's income and thus the taxes it must pay.
The only issue would be that the other freelancers are not 'de facto' employees, meaning they expect you to continuously provide work for them.
In short, I believe the answer is yes - at least for me in Germany, and the UK. The costs would be viewed no more different than your internet connection or other business related expense.
I have touched on this subject (and offer additional advice) in a prior question in the startups exchange
I recommend you speak with an accountant as you could find there are additional expenses that you can write off against your taxes. In addition I recommend liability insurance as you are now exposed to greater risk of things going wrong (from those who pay you, and from those you pay). The insurance will be tax deductible also.
What @morsor says below is also correct - A number of conditions exist whereby a person can be considered an employee. Make sure you and the other freelancers you pay have a contract between you or you could be held liable if they don't pay their taxes (the law could determine you were an employer, thus holding you responsible). If the law determines they are employee's, then their health, sick pay, holiday pay etc could catch you in an uncomfortable position.
Best of luck!