How to extract url data from Reddit API using JSON

You are using the wrong url. Use this:

$.getJSON("http://www.reddit.com/r/pics/.json?jsonp=?", function(data) { 
    // Do whatever you want with it.. 
});

EDIT : Working example based on your fiddle in the comments.

$.getJSON("http://www.reddit.com/r/pics/.json?jsonp=?", function(data) { 
    $.each(data.data.children, function(i,item){
        $("<img/>").attr("src", item.data.url).appendTo("#images");
    });
});

You should use data.data.children and not data.children