There are a ton of voice recording apps available for Android on the Google Play store, but for my money Hi-Q MP3 Voice Recorder is easily the best of them.
Unlike a lot of audio recording software I’ve used on Android, Hi-Q has an extremely clean, intuitive interface that takes just a few minutes to figure out and configure.
The app will record in MP3, WAV, MP4A, OGG and even FLAC, and as you can see from the screenshot makes it easy to see at a glance what format, sample rate, and how much recording time (or disk space) you have left.
Recording can be initiated from the app itself, from a home screen widget, or from directly within the notification drawer. It integrates with Dropbox, so you can have recordings transferred to your Dropbox account. This is a one way sync, however–so after the audio file is transferred to Dropbox, changes to the file on Dropbox or on the local device are not synced further. This feature is useful for copying the file to Dropbox so it can then be deleted from the local device.
I’m not sure if this is just an improvement in recent Android phones (I’m using an LG G4) or specific to this app, but the battery usage while recording seems to be much less than I’ve seen from audio recording on Android in the past. I assume Android phones are just getting smarter about minimizing power usage.
There is a free version of the app that limits the recording clip size to 10 minutes. The Pro version with unlimited recording length is only $3.99.