While there's certainly no shortage of apps you can use to record meetings and interviews, Pio Smart Recorder (free for iOS) differs because it lets you tap to bookmark important sections of recordings.
Say you're recording a conference session. The presenter is blah-blah-blahing about stuff you don't care about. Suddenly, he has a lucid moment and starts talking about something you're interested in -- you just tap your iPhone screen to mark the spot. After 5 minutes, he reverts to the blah-blah-blah, so you tap the screen again to end the bookmark.
Later, Pio lets you go right to the good part instead of forcing you to listen to the full session. You can also use Pio to upload finished recordings to Dropbox or Google Drive (a one-time, $1 in-app purchase). The parts you bookmark are saved as individual audio files (.m4a), along with a file of the entire recording. You can also arrange recordings in project folders. The free app limits you to three project folders, but for $1 you can have an unlimited number.
If you record a lot of audio, Pio could save you some serious time (and agony).
Voice Record Pro (free; $3 removes ads) is another cool iOS audio recording app that's ideal for capturing voices and music. You can record in various audio formats (including MP3 and WAV) and export and import from or to Google Drive, Dropbox, OneDrive, Box and SoundCloud. The app has a bookmarking feature as well.
Both Pio and Voice Record Pro are iOS-only. Easy Voice Recorder Pro ($4) is a quality Android option that records in multiple audio formats, lets you boost input volume and helps skip silent gaps in recordings.
Unfortunately, none of these three apps record smartphone calls. If you're looking to capture calls, check out TapeACall Pro ($10 per year), which lets you record incoming and outgoing calls without paying the per-minute or per-call charges that are common in other similar apps. TapeACall Pro records calls by creating three-way connections between you and the people you call. Some setup is required for each recording as a result. Also, the recordings are processed on remote servers before they're available on your iPhone, but the processing doesn't usually take long.
Call Recorder (free) is a popular Android app that saves recordings to Dropbox and Google Drive and lets you protect access to the app and recordings with a passcode.