Peter was crucified upside down upon his own request as he didn't feel he was worthy to die in the same manner of Jesus. The Pope's chair has a cross of St Peter on the back often leading fundamentalist Protestant groups to imply that it's an inverted crucifix and therefore a symbol of diabolism.Riiiiiiiight.
He is said to have suffered crucifixion at Patras (Patrae) in Achaea, on a cross of the form called Crux decussata (X-shaped cross) and commonly known as "St Andrew's cross" - from Wikpedia.