There is one private key for each bitcoin address. While it is possible to carry private keys around and make payments with them, it is not a very common procedure. The biggest problem is that the person receiving the coins would have to import your private key and transfer them somewhere else to make sure that you don't spend them again (and you would probably have to have an address where you can receive your change).

Bitcoin payments should be made with a bitcoin client (either on your mobile phone or on your computer) because it is simpler and safer. Printing addresses is a good idea for backup purposes. See [this question][1] to find out to print them.


  [1]: http://bitcoin.stackexchange.com/questions/1080/how-to-save-bitcoins-as-paper