"Zen": another light web app for typing.
It's clean enough that I could see it becoming the at-hand writing tool for people who want tranquility when they have to throw open a text editor for a few minutes.
It looks like it uses the browser's local storage to save your typed text and settings. Markdown support if you want it, typewriter sounds if you want those, three well-chosen fonts, and a few colour sets. Export a plain text file when you're finished.
(It looks like this team also makes an iOS notes app, but offers Zen for free on the web.)