Div circular scroll

Be sure to localize all of your variables using var.

JavaScript naming using interCaps is more idiomatic than under_scores.

For a better user experience, use <label> tags on your radio buttons. That makes the ">>>>>" text part of the control, for a larger click target.

If you are willing to change the semantically significant <img> tag into a purely decorative background-image, then the code can be greatly simplified through the use of background-repeat: repeat-x.

$(function() {
  var $scroll = $(".scrollable");
  var w = $scroll.width();
  var pos = 0;

  // Radio button
  var $left_rb = $("#left_rb");

  function rollIt() {
    var movement = $left_rb.prop("checked") ? -w : w;
    pos += movement;

    $scroll.animate({
      backgroundPosition: pos + "px"
    }, 1000, "linear", rollIt);
  }

  rollIt();
});

.scrollable {
  width: 150px;
  height: 50px;
  background-repeat: repeat-x;
}
#scroll {
  background-image: url(//i.stack.imgur.com/vvcpe.gif);
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="scrollable" id="scroll"></div>
<p>Direction:</p>
<form>
  <label><input type="radio" name="direction" value="left" id="left_rb" checked>&lt;&lt;&lt;&lt;&lt;</label>
  <label><input type="radio" name="direction" value="right">&gt;&gt;&gt;&gt;&gt;</label>
</form>

Your code was overall hard to read. But it is somewhat structured properly.

Let's analyse Javascript!

1. Are you afraid of vars?

   Yeah, you don't use a single var. EVERYTHING is a global variable.

   Why is it bad? You are polluting an already polluted object, you allow outside code to mess with your code and it is slower to access global variables than local variables (it's around 10x slower).

   Please, use vars.

2. Your variable names are not that good.

   Some are short, cryptic, meaningless.

   Names like w and dest_pos don't help much. What's w? Can you figure it just by the name?

3. Misuse of the library.

   Why do you have this:

   $original = $("#original");
   $original.clone().attr("id", "left").prependTo("#scroll");
   $original.clone().attr("id", "right").appendTo("#scroll");
   

   When you can write:

   var $original = $("#original");
   var $scroll = $("#scroll");
   $original.clone().prependTo($scroll);
   $original.clone().appendTo($scroll);
   

   The id isn't being used and you can store #scroll in a variable (as you do a few lines after).

4. More library misuse.

   jQuery has something really great going on for it: chaining methods.

   You did it everywhere, except there:

   $scroll.css('left', -w + 'px');
   // Roll it
   $scroll.animate({
     left: dest_pos + "px"
   }, 1000, "linear", roll_it);
   

   You should write it on this way:

   $scroll
       .css('left', -w + 'px')
       .animate({
           left: dest_pos + "px"
       }, 1000, "linear", roll_it);
   

5. Hidden dangers!

   Lets analyse this line:

   if ($left_rb.prop("checked")) dest_pos = -2 * w;
   

   Please, don't eat away your braces.

   Remember the Apple SSL Bug? It was all caused because someone repeated a line after an if without braces. Like yours.

   Please, use braces.

6. Mixed quotes.

   Even though it only happened once, you have to check your quotes.

   Pick between single and double quotes and use the same style, from the beggining to the end of the document.

With all those changes, this is how I would write your code:

$(document).ready(function() {
    var $original = $("#original");
    var $scroll = $("#scroll");
    $original.clone().prependTo($scroll);
    $original.clone().appendTo($scroll);

    var original_width = $original.width();
    $scroll.width(original_width * 3);

    var $left_rb = $("#left_rb");

    function roll_it () {

        var scroll_by = 0;

        if ($left_rb.prop("checked")) {
            scroll_by = -2 * original_width;
        }

        $scroll
            .css('left', -original_width + "px")
            .animate({
                left: scroll_by + "px"
            }, 1000, "linear", roll_it);
    }

    roll_it();
});