Let's not forget the question phrase при чём, which can be translated "in connection with what," "regarding what," "with regard to what," "about what," etc.
Вы здесь при чём?
"With what is your visit connected?" or "To what purpose are you here?" (But it often tends to sound a bit stiff and formal, sometimes with humorous effect -- think of Stephen Fry as Jeeves and you'll be on the right track. In normal colloquial speech, почему is a better choice.)
Also, the Tina Turner bio-film What's Love Got to Do With It? was called Причём здесь любовь? in Russian.
And the negative construction ни при чём could be used as an answer to that question: Тут любовь ни при чём!! ("Love has nothing to do with this!" or "Love doesn't even enter the picture!")