Click here to Buy it Now from the Apple App Store, $1

The plainly titled Synth app features over 40 instruments, a metronome, a sampler similar to the Casio SK1, and a bunch of other cool features like pitch-blend wheel. But all you really need to know is that this app costs a dollar. Sure, you can build it out with some in-app purchases, but the cost of entry is the lowest on this list. Also, the Gorillaz reportedly used it when recording their album The Fall. If it's good enough for Damon Albarn, it should be good enough for you.