The Cave games are really good: Espgaluda II, DoDonPachi Resurrection, Mushihimesama Bug Panic. Though, MHS is more of a dual-stick shooter with bullet hell elements rather than a standard shmup.
Dodonpachi Resurrection Espgaluda II Space Invaders: Infinity Gene Those three are my undisputed top 3 and in that order, but there are some great ports of classic shmups as well: Tyrian R-Type rRootage (there's a very good free version of this, as well as Noiz2sa) and lots of original iOS games that are both cheap and excellent. Assault Squadron Lightning Fighter Ultrablast Astrowings SuperLaser Phoenix WarBlade Icarus-X ISUD Air Attack These are all excellent games. I've listed them in generally the order in which I'd recommend them. They're all worth getting if you're a fan of shmups though.
Medianotzu pretty much nailed it. Definitely get Infinity Gene and Espgaluda II. Haven't yet tried Dodonpachi.
Yup, you can't really go wrong with the trilogy Medianotzu listed (Dodonpachi Resurrection, Espgaluda II, Space Invaders: Infinity Gene). In addition to the other games he listed, here's a few more. Some are better than others, but they're all worth checking out. iFighter Worldly Wings Roswell Fighter Parsec HotField Sky Force Sky Force Reloaded
Darklaga was a game I fondly remember on Pocket PC days, considering how many old PPC games made their way onto the Apple store, I am still keeping my fingers crossed for this great great game.
DDPachi, phoenix, Space invaders infinity gene (really awesome, totally simplicity and the retro flair is there, definitely )
Dodonpachi, Espgaluda, Infinity Gene, Phoenix, Lightning Fighter, rRootage. There's my top must-have shmups.
If you were keen on playing a good iPad shmup... Get "shmup" lol, it's really very good and the developer is addressing all our requests which is nice. Compares favourably to Icarus x IMHO
Download 'Parsec', which has the additional bonus of being Universal and Game Center enabled. Also get the lite versions of 'rRootage' and 'Noiz2sa'. The lite version of Noiz2sa is actually better than the paid version, because of the horrible white background in the paid version. The free version has a dark background where it's much easier to see the action. Go figure.
Space Invaders Infinity Gene has a lite version. Try that, and prepare to shell out for the full version. It's THAT good.
Stick a crowbar in your wallet lol. The games are 1 or 2 dollars each. Except for the cave shmups of course.