SE automatically uploads images to http://stack.imgur.com.

For example, I uploaded the above picture by clicking the Image button and the picture was uploaded to https://i.sstatic.net/vQQKL.png.
As far as .blend files, you can use any upload site. I personally prefer Google drive for convenience, but other people use dropbox and other sites.
Edit (by GiantCowFilms)
We now have Blend-Exchange which is free and dedicated for hosting .blend files for this site.