You might be familiar with the MyScript Calculator, which lets you jot down math problems and solves them on the spot. It's creepy accurate, and now that same technology has been applied to note taking with MyScript Smart Note (for tablets only). It works best if you've got a stylus, but even a finger is accurate enough for this app to figure it out.
There are both write and draw tools in MyScript Smart Note, making it easy to add diagrams and doodles to your notes without the app trying to turn them into letters. The default settings won't turn your writing into a standard font, but it will all still be recognized as individual letters and words that you can manipulate with gestures. To search your notes, you'll want to enable the font translation feature. This app is really great at deciphering all those chicken scratches.
You can play around with MyScript Smart Note for free, but there's an in-app purchase for the full version (a little under $3). That includes unlimited notebooks, unlimited import/export, archives, and more.