Android: The list of robust video editors on Android has been meagre to non-existent for a while. You can do casual stuff with Vine or Instagram, but getting serious work done has been reserved for other platforms -- until now.
Cyberlink is known in the Windows world as making serviceable video-editing software. It's no Final Cut, AVID or Premiere, but it's a step in the right direction. On Android, however, the mobile version of PowerDirector shines. You can trim, cut and split video clips, add transitions, title effects, soundtracks and more.
Unfortunately, the app isn't compatible with a lot of devices, and the UI only seems ideal for editing on tablets. You also probably won't be getting much pro-level work done. For hammering out a more complex edit on the go though, PowerDirector has quickly become an obvious choice.