I am in the early stages of writing an Emacs major mode for browsing and contributing to sites on the Stack Exchange network, in much the same way as dired and list-packages works, with a few inspirations from magit and org-mode.
The problem is, of course, I have no idea how I would interface Emacs with the SE API (v2.1) in the first place. I've never done anything that involves a network connection within Elisp, although I'm comfortable with the language itself (and have taken more than a few looks at package.el).
I've never worked with JSON, although I'm in the middle of W3C's tutorial on it.
A simple 'hello world' would suffice, possibly along the lines of
(execute-json-query "/info")
The W3C tutorial doesn't seem to go over requests, either. I'll have to do my own research on that.
I really don't have any idea what I'm doing; I've only just started feverishly working on this yesterday afternoon.
The problem with other answers is that Stack Exchange API is GZIP'd and url.el shipped with Emacs does not automatically decompress it.
Take a look at my request.el library which supports automatic decompression (to be honest, I just added the support). Here is an example to fetch the most active question in stackoverflow:
(request
"https://api.stackexchange.com/2.1/questions"
:params '((order . "desc")
(sort . "activity")
(site . "stackoverflow"))
:parser 'json-read
:success (function*
(lambda (&key data &allow-other-keys)
(let* ((item (elt (assoc-default 'items data) 0))
(title (assoc-default 'title item))
(tags (assoc-default 'tags item)))
(message "%s %S" title tags)))))
request.el is well documented, comes with executable examples and is well tested.