Skip the online JSON formatters! Run this directly in the vim command line:

:!python -m json.tool

This is very handy when downloading or working with minified JSON and works in your current buffer.

To make it even easier, I set up a shortcut in my vimrc which will run the above command but also set the filetype to json.

nnoremap ,j :set ft=json<cr>:%!python -m json.tool<cr>gg=G<cr>

Note my map leader is , (comma), so ,j (for JSON) will call the function on my current buffer.