If you are one of those people who likes to be ultra-organised you'll love Evernote. To call it a note-taking app really doesn't do it justice. Sure, there is a note-taking element to it, and you can use its mini word processor to draft out documents if you like. But Evernote is so much more – it's an information gathering and organising app.
You can make notebooks to organise your thoughts by topic, and use browser plug-ins to capture stuff direct from the web. You can also email things to Evernote so you can capture messages people have sent you, photos you take, and other snippets of useful information. There are apps for the main smartphone platforms as well as for your PC, and you can use Evernote through a web interface too.
As a seasoned Evernote user on Android, the recent addition that's getting me excited is handwriting support. This is only available in the Android app at the moment, and it is superb. You can make jottings or drawings as notes themselves, or augment text information, or add your thoughts to a photo, for example. It's so useful that I already can't understand how I managed without it before!
OS: Android, iOS, Windows Phone