Can I buy a ticket on United Airlines site if I am from Serbia?

These days, it is rare that you get a paper ticket for your flight. Instead, you usually get an "e-ticket", which is a fancy way of saying that all the information that used to be on a paper ticket[1] is now sent to you by email. This email is sufficient confirmation that you will be on that plane.

At the airport, when you show your passport at the check-in counter (or at the machine), you will receive a boarding pass, which allows you to enter the plane.

Thus, as long as they accept your credit card, you will be able to buy the ticket just fine.

[1] A paper ticket used to be like a little booklet, especially if you flew multiple legs, that contained information about your itinerary, a detailed listing of flight price and taxes you paid, as well as the rules and regulations. However, even though you had a ticket, you still had to go through check-in to receive the boarding pass.

No, you cannot, officially, if your card is issued by a Serbian bank. United.com is only set up to accept payment and passenger information from about 66 countries, and unfortunately, Serbia is not one of them. You may be able to make a reservation, but United will not ticket the reservation without payment, so here are your options:

• Purchase through a third party, such as a travel agent, ticket broker, or consolidator which can accept a Serbian credit card.
• Purchase at an airport with United ticket agents, using a card or cash in the local currency of that airport. Note that an additional service charge will apply, and that some airports will not handle cash transactions.

Jonas is correct in that paper tickets are quite rare these days, but it is not quite right to say that they have been replaced with email. An electronic ticket (e-ticket) is stored in the airline's computers; the e-mail that you receive is merely a receipt confirming your travel details, and your boarding pass similarly is just a piece of paper meant to expedite the boarding process. On a U.S. domestic flight, you will be able to print a boarding pass at home, or at the airport with only your name and some details (PNR number, destination airport, etc.). To fly, you simply need this boarding pass and some carry proof of identity (e.g. passport, military ID, driver's license).