Everybody with an internet connection of any sort with a bandwith of at least 256kbps must pay the fee. The argument is that they can access dr.dk (danish public service television channel), and the content they provide for no additional fee. Obviously owning a TV will cause the fee as well.
It is a fact that almost all danish households must pay the fee, which especially hurts low-income households, such as those of students; the fee is the same no matter the household composition.
There is no good practical reason for not financing danish public service by increasing income tax ever so slightly.
This is how people avoid it in Sweden. However, the stores are obliged to report in when you purchase a TV, but all of these things can be avoided by simple lies ("I gave the TV to my friend for his birthday"), and many do so.
The declaration - however - is legally binding and there are huge fines for breaking such a declaration. However, they must be able to prove that you do actually have such devices, by entering your property. In most cases, they don't really bother, though.