I often get asked about what app I use for dictation on my iPhone. There are lots but my favorite is, without question, Dictate+Connect. This app has a great iOS7-y look and feel and has more features than I've had in a handheld recorder. I can easily adjust the recording quality, mic sensitivity and playback speed. It also has a voice activation mode that automatically stops the recording when I pause to think, which in my case is often. The app displays a waveform of your dictation while recording. It exports to WAV, AAC, WAV IMA4, and AIFF and there is a native version for both iPhone and iPad.
On the sharing side, Dictate+Connect lets me share my recordings via email, export, or in a separate iOS app. For example, I use the Quickshare feature to send dictations (in WAV) format to the transcription ninja at my office. I also send WAV files to Transporter (or Dropbox) to transcribe with Dragon Dictate on my Mac. I still use a physical pocket recorder but am using Dictate + Connect more and more. Because it is an app, it's always in my pocket.