well, I doubt you will find final fantasy or pokemon for the iphone, but I would recommend Nanosaur 2. By far the best iphone game I have played. Maybe angry birds... but I'm not all that into it, but it's very popular.
Well in the form of small apps that just help pass the time, I would reccommend Jetpack Joyride, 4 Pics 1 Word, Temple Run 2, Final Fantasy Crystal Defenders, and Paladog. If you want a big game with an actual story, you should try The World Ends With You Solo Remix. Those are a few of my favorites, which can be attained without hacking or modding for cheap prices on the AppStore (exceptions are: Crystal Defenders=7.99, The World Ends With You=15+)