Most countries are Visa free for stays up to 90 days. If you stay at a private residence you will have to register at the local police station within 24 hours. If you stay at a hotel the hotel will complete the registration online. With the registration you will be given a white card that you are required to carry with you. It is best to carry it in your passport. Police here are allowed to conduct random identification checks which are usually conducted at road side check points or when the police do checks on bars and clubs.
If you have US visa, or EU residence permit you can enter Serbia without a visa. This is something new. They told me this in the Serbian consulate in Paris. Apparently it is all well explained on the webpage of embassy of Serbia in UK.
