RFID tags can either be passive, active or battery assisted passive. The active or battery assisted passive tags will transmit an ID where as the passive RFID tags have to be powered via the reader.
I took a look at a cheap RFID reader for the arduino, the RF10-RC522 which can be purchased for around £5 and comes with 2 example RFID tags. The cards in the kit are passive.
It is possible to do RFID Card reading and writing on the Arduino and you can get a code samples from here: https://github.com/miguelbalboa/rfid or you can also find a guide on using the RFID cards with Arduino here: http://www.grantgibson.co.uk/blog/2012/04/how-to-get-started-with-the-mifare-mf522-an-and-arduino/