Some apps cry out for innovative flourishes, but what you want from a note taking app is pure simplicity. From the makers of WordPress comes Simplenote, a minimalist note taking app that syncs notes across all your devices.
The driving ideas behind Simplenote are speed and efficiency. Open the app, compose your thoughts using the onscreen keyboard, and the app will automatically hang onto them for you. Feel free to segment your notes using tags if that helps you organize your thoughts. There's also a search function if you really need to find that one time you wrote about "elephant toe jam".
The ability to sync across devices is the extra-attractive aspect of Simplenote. Signing up for an account - which is free - on the Simplenote website should be enough to let your entered notes freely flow from one device to another, no matter where you choose to access them.
Unfortunately, however, I couldn't get the sync to work for myself. The notes I wrote on my mobile device never showed up on my desktop web display and vice versa, even though both versions appeared to be constantly in the process of syncing. I concede that this may be an issue specific to my devices since I don't see much complaining in the comments, but it was definitely disappointing not to have it work for me.
Automattic Inc.'s Simplenote is an ideal, minimalist note taking app that can (maybe) sync across devices - it's free, so give it a go and see if it works for you.