For Google Docs-like tasks I prefer a combination of Org and git. Org is a powerful-but-easy-to-learn document structuring language. You ca write it in any editor, but in an Org-aware editor your document really comes alive. The oldest, most feature-complete implementation is in Emacs. Org documents can be exported to virtually any final format. I don't specifically recommend git so much as any distributed VCS, to sh…
Your comment implies that there are other editors, besides Emacs, supporting Org mode... Could you please elaborate on this?
- On my Android phone, I use Orgzly to capture notes, tick off finished tasks, and see various filtered views of my agenda.
- I see there are implementations in Vim, namely Vim-OrgMode and VimOrganizer.
- If you want to embed something on the web, org-js is supposed to be good. There is also the GitHub editor, of course.
- Further out of my comfort zone, there is something for IntelliJ IDEA called org4idea, and I saw you should be able to get orgmode support in Sublime Text. I also found Organized for Atom, but that appears to be a sort of Markdown-Org mashup, so not necessarily the right thing.
- Then, as unwelcome as this last point may seem to some, it's worth pointing out that Emacs is not an editor in singular. If you don't like the default editor that ships with Emacs, there are other editors to choose from which all run in Emacs. This includes the seriously fantastic Vim port called Evil. From what I can tell, the AutOrg project is even specifically packaging Emacs+Org in a way to make it more approachable to beginners.
Note that many of the options have not successfully replicated the full Org feature set yet. However, in the context of this discussion I have limited myself to the features that are also supported by Google Docs, which are... not many.