Do RFID tags have a "real" processor capable of simple computations? If so, what is the processing power of nowadays RFID processors?
That depends.. RFID is a very broad field.
There are very simple tags that really only send back their ID when activated using a fixed function logic. I doubt many of them are still in use.
And then there are very sophisticated ones that even run programs written in JAVA and have crypto-processors and other funky stuff built in.
One example of this is the SmartMX Mifare card from NXP.
http://en.wikipedia.org/wiki/MIFARE
Note: Don't confuse active and passive tags with processor/no processor tags. A tag is active if it has it's own power supply. That does not imply that it has a processor and vice versa.