This app was mentioned in 7 comments, with an average of 1.86 upvotes
Late to the party, but if you're a musician, ChordBot (Play Store link) is an invaluable little tool. I use it when I'm not at the piano to play around with chord progressions to get ideas. You can layer different instruments/drum patterns, use any inversions you like, use any type of chord, change the arpeggio style, yadda yadda yadda.
I like to use Chordbot to capture basic chord progressions when I'm away from my instruments. You won't be able to do anything with guitar tabs, but it's perfect if you want to create basic song structures or experiment with different chord progressions quickly.
One of my all-time favorite Android apps is Chordbot. I've linked to the free version, there's a paid version as well. Just set up your chord progression, and figure your melody out while it loops.
On a whole other plane, but a very approachable one, you can get Reaper, an entire Digital Audio Workstation (DAW) for $60. (And if you don't pay, you just have to wait ten seconds every time you load the program, but you should pay, because they're awesome.) A DAW will allow you to create music however you want to; it's what they use in music studios. You can make music piano-roll style, or play a MIDI keyboard into it, or record vocals our acoustic instruments, and mix them all together.
Leveraging the power of a DAW has a pretty steep learning curve, but it's incredibly worthwhile. Once you get it configured, and you download a bunch of virtual instruments (VSTIs), you'll be amazed at what you can do.
I know it's more complex than you were probably wanting, but learning to use a DAW will open up infinite possibilities for you. Put up with a couple of weeks of frustration, and even without a musical background, you can really start using the tools in the DAW in your workflow. It won't end up just being a crutch; as you learn more about music, knowing about how to use a DAW is invaluable.
/r/Reaper has a few tutorials in the sidebar, and you can find tons of helpful information on Youtube. You can also check out other DAWs that might suit your style better; I've been using Ableton lately, which is astounding. Reaper is a great place to start, though; grab the 30 day demo and start messing around. Read through the manual, do a few tutorials, and I think you'll find it worthwhile.
Android
chordbot for a fancy metronome.
Audio Evolution DAW
gStrings guitar tuner (now that it can be used for multiple tunings)
miidio for quick recordings
SoundHound to identify something I don't recognize.
Mac OS X (but these are available on other platforms)
ExFalso for editing tags
TuxGuitar for writing tab - this will emit ASCII tab which is convenient for putting tab directly into reddit comments.
iOS (on my old iPad)
Chordbot Lite | 4.5 rating | Free | 1,000,000+ downloads | Search manually
> Chordbot is a music app that lets you create and play complex chord progressions quickly and easily. Use it to: * Experiment with advanced chord progressions without instruments or fingering charts. * Create customisable backing tracks for instrument ...
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I use Chordbot Lite to loop chord progressions as backing tracks and play over them. Pretty handy.
https://play.google.com/store/apps/details?id=com.chordbot.demo.gui
Chordbot Lite is exactly what you're looking for :)