Hm, that is one of my older "language" problems. Shouldn´t it be called "The King and Me"? I think that was what we´ve learned at school. But on the other hand that´s a long time since then - so I could get that mixed up.
Not to worry, even native English speakers get it wrong. It depends on whether the pronoun is the subject or the object of the sentence.
"The king and I got drunk last night. The royal bartender served flaming Aber Guts to the king and me all night long."