I've spent a somewhat embarrassing amount of money on music and synthesis apps for my iPad. Not all of them are jewels. I won't name any names here, but I'll warn that it pays to shop carefully, and to look at the app developer: is the app developed by one person who's just kinda futzing around with an idea, or by an actual company? The latter is preferable if you are hoping for any kind of support / bug fixes / feature updates.
The exception is, of course, free or $0.99 apps. For $0.99, who cares if the developer lives in his mom's basement in Belarus? (although it's sad to run across a $0.99 app that's *almost* perfect, which you know will never be updated or fixed).
Having said all that, I'd like to attempt to steer you, dear reader, towards the exceptional synthesizer and sound generator apps that I've encountered. Many of these cost $4.99 and up -- but they're worth it. (note: after one buys an app, it can be a bit difficult to determine the current price of the app -- some of my prices might be off.
Animoog for iPad $9.99 - A subtly seductive little synthesizer that didn't really impress me until I'd noodled with it awhile. It has an interesting synthesis paradigm, kind've like vector synthesis over a set of wavetables -- I suspect Moog will continue to add voices to this and really expand the kinds of sounds it can make. Also of note: it has a really charming kind of retro-Buchla keyboard that (among other things) registers the position of your finger along the length of the key, thus offering another control parameter on a per-note basis.
Animoog for iPhone $0.99 - If you just want to stick your toes in the water first, the iPhone version is cheaper and has all the same featurers, just the misc control panels are organized differently for the smaller form factor. This version also runs on the iPad, BTW.
Alchemy free / $14.99 upgrade to Pro - This offering comes from Camel Audio, who have a very solid reputation in the VST and soft-synth biz. It doesn't look like much at first, but if you start playing with it, it "comes alive". I haven't upgraded to Pro (yet) -- the app has a storefront that you can purchase additional waves / sounds for $4.99 a pop. This may sound like a lot but so far I've been impressed: some very high-quality sound design goes into these voices. Mac/PC/VST versions available.
Sunrizer $4.99 - If you can find a better iOS synthesizer for $4.99 --
buy it! But seriously -- you won't find such a thing. Sunrizer has a really great synth "feel" with great sounds for a great low price -- it's one of the best values on this list.
Addictive Synth $9.99 - A bit pricier than Sunrizer -- think of it as Sunrizer's twin brother who's kept in the attic. Great sounds, great feel.
Sylo Synth free / $3.99 upgrade to Pro - An inexpensive app that uses "granular synthesis" to produce sounds. The free version has advertising and lacks a few features, but it'll give you a taste of what you'll get if you go "pro". Not as nuanced as some of the other synths listed here, but one of the better / simpler implementation of granular synthesis I've seen.
Argon $1.99 - A good basic synth that will surprise you with the number of parameters it offers. Not really my favorite but it's a steal at $1.99.
The apps above are all kind've "standard" in that they have keyboards and relatively low learning curves. The apps listed below are "paradigm breakers" that can make some marvelously twisted, complex sounds, but you need to throw caution to the wind and experiment and *gasp* perhaps even read some documentation before you'll feel comfy with them:
Moog Filtatron $4.99 - If the VCS3 was a synthesizer, then I suppose one can call the Filtatron a synthesizer, too. Maybe. The name doesn't matter -- Filtatron is great for making all manner of "soundscapes" - it's difficult to describe. Musical toy or Pro SFX generator? I think it's both.
Jasuto Pro $4.99 - Here's where we
really begin to leave planet Earth. Jasuto is a bit like a modular synth in that it allows you to connect miscellaneous sound functions together in an arbitrary manner ... but then it gets weird. One nice feature is that it connects to a user repository where people share their creations. Not for beginners.
Also available as a VST module.
CrystalSynthXT $4.99 - I'm still not really sure what to think of CrystalSynth. It's got a lot of "standard" synthesizer controls, but the controls can be automated and -- well, in the end, you can make all kinds of cools sounds with it. It also has a "morph" function that allows you to "marry" two different patches and listen to what their children sound like.
Also available as a VST module.
Reactable $9.99 - This one is a bit like Jasuto Pro (above) but a bit easier to comprehend. You build small 'systems' out of samples and oscillators and other components, and then let it play. If you do it right, you can build a system that's interactive, ie, where you really can play it by turning the shapes and moving them around. Also like Jasuto Pro: not for beginners.
So far, these are my favorites. There are many many other music apps out there: MIDI utilities, micro-studios, sequencers, alternative controllers, etc. But today I'm limiting myself to synthesizers and sound generation apps.