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Well "When the Saints Coming Marching In" is a good place to start, it's probably one of the simplest harmonica songs you can learn.
In fact, I was at a Guitar Center the other day and decided to pick up a small pocket harmonica, since I thought I'd make the trip worth more than some new strings for my acoustic, and the box had a slip of paper that showed how to play that very tune.
From that one song though, you can even branch out, make the notes last longer in places, let yourself find tunes to add on that make it sound better.
Hope I offered some sound help.