[susan53]

Yes - logically Mark is absolutely right, but people do use "me too" to mean I'll say the same about you. Mark, if you say to your wife I love you and she replies Me too - do you really understand that she loves herself? (And I very much hope you don't destroy the moment with a lecture on grammatical logic!)

A funny story - I had an aunt who said "me too" all the time. At one point there was a whole tribe of kids between 0 and 3 in the family, and she was chief babysitter. She said it so often that one of them interpreted it as being her name and started referring to her as Me too. It stuck, and the whole family called her Me too from then on.