The Catholic Church believes in the existence of guardian angels. Here is the official teaching, paragraph 336 of the Catechism, at the end of a chapter on angels:
From infancy to death human life is surrounded by their watchful care and intercession. "Beside each believer stands an angel as protector and shepherd leading him to life." (Saint Basil) Already here on earth the Christian life shares by faith in the blessed company of angels and men united in God.
Our priest mentioned guardian angels in passing the other day, and I had the amusing mental image of Rosie's guardian angel arriving at the hospital and having to introduce itself to Katie's and my guardian angels.
Also, when I was at work learning about how to find missing payments, I had the amusing idea of a prayer limbo, like huge filing cabinets filled with prayers which weren't able to be assigned to anyone or got rejected by their recipient.