For my Android application, I have to upload videos in all kinds size to some cloud system to not exhaust my very own server. I'd rather not change my code a lot. And So I am searching for a method to publish personal files through HTTP web service. Are you aware what's the best alternative with this?

You should think about Apache HttpComponents. I will help you to formulate the Publish request. I'm not an Android Developer, but knowing the search engine results, it's available to work with.

For me personally, the best choice is by using FTP. You should use Filezilla, it's FREE and simple to use. :)