This should prove to be a popular one - a native Backgammon game for the iPhone and iPod Touch. 

It’s still a very early release, and seems a little rough round the edges - but then again when I fired it up I realized I don’t really remember how to play properly, so I just dorked around with it for a few minutes.  It does offer a choice of playing against the iPhone or against another human player, and its developer is promising some new features soon.