Alain De Botton's commonsense explanations of the ideas of Socrates, Nietzsche and other heavy-hitting philosophers is a great introduction to philosophy.  He explains the ideas, the men behind them, and their wider impacts in a down-to-earth fashion accessible to all kinds of readers.   He also does a great job of giving them context and explaining why, though they were born perhaps thousands of years ago, these ideas are still vitally important in the modern world.

Nothing beats the original source material, for sure, but everybody needs a little help cracking the covers from time to time.  De Botton's book is not "Philosophy for Dummies" -- it's just an enjoyable way to get a textured introduction to the subject.