There are basically two kinds of people who want to write things in plain text files: those who have to deal with weird, intractable cross-platform formatting issues, and those who just like the simplicity. Text files don't have bold, italics, header sizes, margin tabs, or anything that might get lost in travel from one word editing tool to another. Text files just have text, and I love them for it.
But text files are files, and you can lose them. You can upload or sync them to cloud services like Google Drive or Dropbox, but they're usually treated like any other file. You can usually preview them in the web version of Dropbox or Google Drive, but to actually edit them, you'll need to download them, edit them in a preferred app, then sync them back. If you're on a computer without your synced-up Dropbox or Drive account, or on a mobile device, you're out of luck. Unless, that is, you know about these perfect text-minded apps.
Here's how to get at and edit text documents in Google Drive and Dropbox, in nearly any reasonable situation. Note that, across most screens, you can usually preview (read and copy) plain text documents, so it's really live, synced-up editing we're after.
"I only have my phone or tablet, and I need to edit a .txt file"
If you're a Dropbox user with an iOS device, you're somewhat in luck, as Dropbox is the preferred storage solution for all kinds of writers who like to tap out ideas on iPhones and iPads. The Unofficial Apple Weblog rounded up a whole bunch of iOS/Dropbox text editors, and I agree with their number one pick, PlainText. It's really simple, it's got a simple and paper-themed interface, and it's free if you don't mind advertisements, cheap if you'd like to remove them.
The official Dropbox app for Android installs a companion application, "DB Text Editor," that allows you to make very simple edits to any text file in Dropbox. Need something a bit more robust? I recommend the Dropbox-syncing Epistle app, which, like PlainText, makes the Dropbox syncing a background feature, and gives you just some text space to write and edit. If you're a Markdown/HTML nerd like myself, it has live Markdown/HTML previews, which is a nice bonus.
Got .txt files in Google Drive? For Android, the thing you want is Jota Text Editor. The Drive app itself can't edit plain text files, which feels strange. But you can click and open the file in Jota+, edit away in a robust, smart editor, and when you're done, "Share" the file back to Drive. If you dig Jota+, and want to use it to directly edit and save files to Dropbox, Box.com, or SkyDrive, you can grab Jota+ Text Editor, and pay $5 to unlock its full cloud-syncing powers with a license key.
On iOS devices, the choices are basically limited to Quick Office Pro on the iPhone or Quick Office Pro HD on iPad. Both can connect to Google Docs/Drive to access files, and both can handle editing plain text files. It's one of many good reasons Google acquired Quick Office for its own app development.
"I'm on a browser and need to edit a .txt file"
The best solution for web-based Dropbox text file access is TextDropApp, a web-based editing tool that syncs to Dropbox and works in any reasonably modern browser. It's not free, but you can try it out with a full refund guarantee for 7 days. And the sooner you sign up, the less it costs--it's $8 per year at the moment.
If you're a Chrome devotee, you have other options, both of them free. Drive Notepad for Chrome creates, edits, and resizes text files inside Google Drive for your eyes and fingers. On the Dropbox side, I prefer SourceKit, which has all kinds of tools for programmers working on code files inside their Dropbox accounts, but which works just fine for editing plain test.
Not everybody needs to edit text files and keep them saved and secure up to the minute, but those of us who do appreciate smart tools for doing so. Do you do your own plain text file work? What do you use to get the job done? Tell us about your picks in the comments, or tweet at me, and we'll compile good answers for a follow-up.