In Germany, every household has to pay €17,50 per month (€210 per year) as a fee to receive television and radio broadcasts (also through the internet, for more information see the Wikipedia article).
Once you officially register in a district office, you will be in the system and will eventually receive a letter saying you have to pay. This letter may come two years after you have moved in, and they will then ask you for the fee for all that time at once (2 years = more than 400€).
Now the law says, every household has to pay. As every floor is sharing one bathroom and one kitchen, every floor counts as one shared flat, i.e. one household. That means, only one person on a floor needs to pay the TV licence fee and all the others can refer to him. Of course, you should in that case share the fee. If you're for example nine flat mates in one floor, the TV fee is €23,33 for each person per year. Not comparable with €210 per year if you pay it on your own.
You can use this letter rundfuck_vorlage.pdf (also available as .odt file: rundfuck_vorlage.odt) as example of what to answer in case they want you to pay the TV licence fee even though there is already someone else on your floor paying for it. I used this exact letter, only filling it out with my data, and it worked.