My 2015 New Years resolution was to create one song a week using only an iPad. As a producer, I was curious to learn what challenges iPad musicians faced including songwriting, performing, recording, editing, mixing and mastering. 52 weeks, 52 songs later, I learned that the biggest challenge was figuring out which apps are the friendliest to use.

Here'a my list organized by product category:

Studio in a Box

Korg Gadget is my favorite iPad music app of all time. Yes, it's expensive but soooo much fun and it curiously strikes this balance between structure and customization.
Cubasis is truly a band-in-a-box. It offers the best digital audio workstation (DAW) and pretty much interfaces with everything. If you've graduated from Apple GarageBand and wish you could use Logic Pro or Pro Tools, Cubasis is your best bet.
Auxy is a fun app. Nice UI and fun to use.
Metronome is a great keeper of time. Yes, most apps have a built-in metronome but if you're looking for something stand-alone, I recommend this one.

Beats

IMPC Pro is the only drum sequencer you'll ever need. I use this app for everything. The default sounds are great and you can also load new sounds through the iTunes interface.

Guitar

Bias Amp is perfect for any guitarist interested in achieving a nice, vintage sound without spending thousands of dollars. What's uniquely cool about this product is that there's also a social feature where you can create and share your "guitar sound". There's also a free marketplace where you can download guitar sounds from other noteworthy musicians.
JamUp Pro is a nice companion to Bias Amp â€“which helps you record your sonic ideas. As where Bias focuses on helping you craft your sound, JamUp Pro is more of a workbench for guitarists. This is where you'll find a tuner, a metronome and a recorder.
Flux by Arian Bellow is perfect for any guitarist interested in researching and discovering new sound textures. It's a clever app that quickly helps you create new soundscapes without spending hundreds of dollars on delay pedals, chorus, phasers and more.
Ultratuner is pro worthy. I use this app to adjust the intonation of my guitars.
Silvertune is a really nice guitar tuner. What I like most about the app is the section with alternate tunings.
Amplitube gets the job done. The sounds are great and the recording studio section works well.
MIDI Guitar 2 is awesome. Pick up your guitar and start recording straight to MIDI. From there, you can drag your MIDI track to Cubasis, Logic or Pro Tools and start building entirely new soundscapes.

Keys

Korg and Arturia make excellent products. I'm not a fan of skeuomorphic design but I appreciate how much work was put into these apps.

Korg iPolysix is great for retro sounding music. If you want to compose for an 80's retro video game, you'll love this app.
Korg iMS-20 is perfect for people who want to mess around with patch bays and oscillators. It's really heavy on the technical side but if you're a gearhead, this is a good app.
Korg Module has a very nice sounding piano. It's probably the only piano app you need.
iM1 is great for composing electronic music. The extra sound banks are totally worth the price.
iProphet, iSem and iMini Synthesizer are all great sounding apps and an affordable alternative to Arturia's desktop collection.

Side Note
Arturia's desktop collection is AMAZING. Really, it's the only piano/synth/keyboard package you'll ever need.

Music Production

AudioBus is essential if you ever want to start combining music app together. For example, maybe you want to use Bias Amp for your guitar sound but then run it through Final Touch to later record it on Cubasis.

FX

Filtatron by Moog is great or FX. I would plug this into the FX portion of AudioBus and run guitar sounds through it.
iVoxel is a vocoder. It's great for manipulating your voice. It could really use a UI touch-up but the product is still good overall.

DJ / VJ

dJay 2 is my favorite DJ app. What I love most is that you can link it to your Spotify premium account and start mixing instantly.
Pacemaker is perfect if you're ever at a party and you just need to create a quick mix without a whole lot of effort. It has this stand-alone mode that's awesome.
Traktor is a good app but I didn't find myself using it much.
Gliese is perfect for DJ's who want to present cool animations during their set. I didn't really need this but it was fun to sometimes just project cool visuals while creating music.

Hardware

iRig Pro is a godsend. It was the easiest way to record vocals, guitar and keys from a midi controller. It offers 3 different connections so that you use both older and newer iPad connections.
Oxygen 25 may be the only MIDI controller you need. It has built-in drum pads so that you can link that with IMPC Pro.

`Apps I Do Not Recommend`

AudioCopy cannot deliver on it's promise. It's buggy and always crashes. I wasted too much time trying to get this app to copy files. I ended up simply using Cubasis for everything.
Final Touch aims to help you master your song and it's cool but not very helpful.
Garage Band is a good app but it becomes very limiting very soon. I found myself wasting a lot of time trying to work with "the Apple way" instead of just being creative.
musicIO has a good pitch and I really wanted the app to deliver MIDI over USB but I never got it to work. It's expensive and I still suggest MIDI Guitar 2.
MIDIMux again hold the same problem as Music IO. The UIX is unnecessarily complicated and it doesn't always work. The price point is high and not worth the stress.
Neo-Soul Keys has really nice sounding instruments but they're way too expensive.
SampleTank works well on a desktop but the UIX is lacking on an iPad.
Pocket Studio has a nice set of features but I found Cubasis to have a better UI, FX and media management.
Focusrite Tape has a good pitch but the UI is awful. I wish I could redesign this app.
Boom 808 and Boom 909 are good enough drum sequencers but you just don't need them if you take the time to learn IMPC Pro. Trust me, when you're writing for iPad, you want to learn as few apps as possible.
Rhythm Studio is terrible. The apps don't integrate well with each other and it's lame.
Rebirth deserves some mad respect but it's terrible for iPad.
Tabletop is more of a store than a musical tool. I don't mind pay for in-app purchases but I think this company took it too far. There's very little you can do without shelling out cash. This app neither only made me poorer overall. Poor financially and creatively. In contrast, Korg Gadget is expensive but the app is fun to use and can help you writing music quickly.