Benjamin Franklin has been credited with the origin of this idiom in some places but it actually showed up in the 17th century, in George Herbert's Outlandish Proverbs, circa 1633: A penny spar'd is twice got. It's meaning hasn't changed through the years and is quite clear, it is as useful to save money that you already have as it is to earn more. ( source )

There's a theory that the phrase saved by the bell means a way for people mistakenly buried alive to save themselves. In Victorian times a grave was equipped with a bell that had a string that was tied to the dead person's finger. Then if they woke up and found themselves in a coffin they could ring the bell and be rescued. I like the theory, that's smart thinking. But alas, while that is something they did in Victorian times it isn't where the phrase comes from.  The phrase actually comes from the boxing ring. Click here to read more about it.  And when we use the phrase these days we are saying that we have been saved from something just in time, just before it could have gone wrong. 

This phrase traces back to author Anthony Trollope and his book  The Kellys and the O'Kellys , published in 1848. The line, slightly different than the phrase as we know it now, read this way:  “If it was to save my life and theirs, I can’t get up small talk for the rector and his curate.” It means that if my very life depended on completing a task or something then I would most likely die.

Especially important in Asian cultures is the idea of saving face. You can read about the origin of this phrase here . The phrase means to protect, shelter, or save someone's reputation.