What exactly do you want? To store many types of files? Do you want the service to be decentralized and censorship-resistant? Go here: http://wordsalad.info/storesharing.html#file-sharing
This site has different subsections for storing videos, images, txt files, etc. Go to TOC at top of page to see the sections and jump to them.
There is also Microsoft's One Drive but I wouldn't trust it.
EDIT. Oh, I forgot! http://mega.nz of course! It supports many file types and a user can download a whole folder if they wish. For downloading larger files or folders you must use the app as browser decryption buffers are too small on Firefox.
I need something that works exactly the same way as Google Docs
Try this link. It has lots of online document editors of various types. http://wordsalad.info/storesharing.html
(post is archived)