In addition to the various notes apps, I'm also looking at an app called MyScript Stylus.
http://www.myscript.com/stylus/
It's not a note-taking app per se, but rather a handwriting recognition keyboard that works in basically any app where you can type. It recognizes your handwriting and converts it to text as you write. It's very similar to the old PalmPilot stylus input system, only 1000x better, faster, and more accurate.
I've used it with Apple Notes, OneNote, and MS Word so far, and it works very well with the Apple Pencil. For those of you who would like to convert their handwriting to text, this might be a good option, and it's FREE! Since it is basically a keyboard addition, in order to use it you will have to enable it by going to Settings, General, Keyboards, Add Keyboard and selecting it. Once installed, you can choose it from the Globe menu on the keyboard.
NB: The developer MyScript has other apps in the app store that might also be useful for people who need to insert drawings or other objects, math formulas, musical notes, etc. Worth a look.
http://www.myscript.com/