Peter the apostle is Saint Peter, right? If so, then he requested that he be crucified upside down as he felt that he wasn't worthy to die the same way as Jesus http://www.seiyaku.com/customs/crosses/peter.h tml
It's interesting that Peter thought himself unworthy to die as Christ did - even though crucifiction was a common criminal's death in Roman times, so hundreds of thousands of petty criminals met their death in this terrible way. It was not a unique death for Christ - part of the whole of point of him living and dying as a man.