I have tried many Audio Recording Apps, most which either do not work, or are only for recording pre-selected Radio Stations.
I have found two that work, but only record from the microphone, so any external sound will also be recorded (phone, knock on the door, children, dogs, birds, cars, talking, music, coughing, laughing, etc.). These are the only two apps I've found that will work with my Samsung Galaxy Note 3, running JellyBean 4.3:
>>> HiFi Corder (m4a or aac format)
>>> ASR (wav files)
I've tried these apps, which do not work on my Note 3: AudioTweet (freezes), AutomaticAudio, AutoSoundRecorder, RadioRecord (Russian only), RadioRecord (Spanish only), RecForgeII, RecForgeLite, Record (Internal App Error), Record4Me, RecordOne (Korean only, no menu), TapeAudioRecorder, Urecord, SoundRecorder, SoundRecored+, AdvancedAudioRecorderBeta, Rec.Radio (only preselected stations), SmartVoiceRecorder, zRadio.