I typically use the voice memo app because it's easy and the quality is pretty good.
For more options, the Voice Recorder Pro app is great. You can specify some file format options, and you can export (cloud & wifi) and/or email the recordings.
For a bit of money, you can buy a Shure MV88 microphone, which has it's own app. The cool thing is it's a multipattern stereo microphone, so you can get directionality out of it. So like if you set it on the table between you and someone else, then you can record them in one channel and you in the other, which makes it easier to hear just yourself, or just them, later. Or at a workshop you could dial in a tight angle and point it at the presenter to reject all the people near you. It can also make mid-side recordings, which can be really great when you're recording videos. In the US it's about $150 now. For the same money you could buy a handheld recorder, but the recordings wouldn't be as good as the MV88.
Shure has a short demonstration video if anyone is interested:
http://www.shure.com/americas/products/ ... microphone