Backgammon Guru Pro 2.99 USD: Backgammon Guru Pro: a great app for your iPhone, iPad, iTouch. Backgammon Masters is your starting place, find thousands of players from all over. IPad is an iOS -based line of tablet computers designed and marketed by Apple Inc.
It's the iPad equivalent of the PC software 'extreme backgammon' which is probably the strongest backgammon program currently. Don't waste harrahs your time with apps like Backgammon NJ, as the app is not only poorly designed but.
For playing with other people over the Internet, then 'Backgammon HD' is your best bet. For playing a strong computer opponent, 'XG Mobile' is currently the best.
Response to Hans Achen: You need to pay more attention to accuracy. Look at my first sentence, my comment regarding 'Backgammon HD' is 'for playing other people over the internet'.
I then clearly state which app I think is the best if you want a strong opponent. You should think before writing nonsense.