Do you like old-school shooters? If so, Dodonpachi Resurrection is the game for you! Cave has brought out another awesome shooter on the iPhone (the first being Espgaluda II).
There are two game modes in DoDonPachi. The first is iPhone mode which is a great way to jump in and play. It uses a hit variable to determine the strength of your weapons (the slider is indicated in the top right) and has an interactive hypermode to unleash the ultimate destruction on your enemies. The other mode is Arcade. This mode has you pick the fighter style you want and requires a bit more strategy while playing since you don't have the freedom you have in iPhone mode. You can also configure how much screen is displayed while playing (I am partial to large so I see as much of the screen as I can) as well as button placement for attacking enemy ships.