One of my favorite jokes: A flood comes, and a pious man is stranded on the roof of a house, and he prays to God to deliver him. Soon enough, a boat shows up, but the man says, "No, thank you - the Lord will take care of me." This happens again, and then a helicopter comes by, but he sends them both away. Finally, the waters wash him away and he drowns. When he arrives at Heaven, he complains to St. Peter, "I put all my faith in you, and you abandoned me. Why?" St. Peter replies, "Heck - we sent 2 boats and a helicopter. There wasn't a whole lot more we could do."
Sometimes the Lord works in mysterious ways - like, through helicopters and dialysis machines...
Edit: and as counterpoint, I also like the gag where the inmate is praying in prison for delivery and then someone comes to break him out and he prays, "Oh - never mind. Thanks, anyway."

Can't remember what that's from, though.