I would assume actually that services should be "Stateless". They maintain the state within themselves but when they give over the data to another service or another business process, they no longer hold the state of data.

I would love to know where you would like to see "stateful" services? a real life example?

I am interested in knowing for what purpose a 'stateful' service was implemented. 

To clarify, I would consider a stateful Web Service one that exposes a SOAP Method which you first must call in order to receive a token.  You would then need to pass this token in all subsequent SOAP Method calls, thus 'preserving state'.