Bookmarklet which creates download links on *any* Soundcloud page. Full credit goes to duncanbeevers, see https://gist.github.com/2157987 -- Last tested on newer Soundcloud site: 24 Jan 2013 Successful :-)

sc-dl-min.js

(function(a){var b,c,d,e=$(".sound"),f=require("config").get("client_id"),g=require("lib/connect").getAuthToken(),h=require("lib/helpers/conversion-helper"),i,j,k,l,m;for(b=e.length-1;b>=0;b--){c=$(e[b]);if(0==c.find(".sc-button-download").length){var n="https://soundcloud.com"+(c.find(".soundTitle__title").attr("href")||a.location.pathname);k={url:n,client_id:f},m=function(a){return function(b){var c={client_id:f};l=require("lib/url").stringify({query:c},b.stream_url+".mp3"),d=a.find(".sound__soundActions .sc-button-group"),j=d.find(".sc-button:first")[0].className.match(/sc-button-((?:small)|(?:medium))/)[1],i=$('<a class="sc-button sc-button-download sc-button-icon sc-button-responsive">Download</a>').attr({title:"Download this sound ("+h.bytesToMB(b.original_content_size)+")",href:l}).addClass("sc-button-"+j),d.append(i)}}(c),$.getJSON("http://api.soundcloud.com/resolve.json",k).success(m)}}})(window)

sc-dl.js

(function(window) {
  var i, $sound, $buttonGroup;

  var $sounds = $(".sound");
  var clientId = require("config").get("client_id");
  var oauthToken = require("lib/connect").getAuthToken();
  var conversionHelper = require("lib/helpers/conversion-helper");
  var $downloadButton, size;
  var params, downloadUrl, onSuccess;


  for (i = $sounds.length - 1; i >= 0; i--) {
    $sound = $($sounds[i]);

    if (0 == $sound.find(".sc-button-download").length) {
      var soundcloudUrl = "https://soundcloud.com" + ($sound.find(".soundTitle__title").attr("href") || window.location.pathname);

      params = {
        url: soundcloudUrl,
        client_id: clientId
      };

      onSuccess = (function($sound) {
        return function(data) {
          var params = {
            client_id: clientId
          };
          downloadUrl = require("lib/url").stringify({ query: params }, data.stream_url + ".mp3");

          $buttonGroup = $sound.find(".sound__soundActions .sc-button-group");
          size = ($buttonGroup.find(".sc-button:first")[0].className).match(/sc-button-((?:small)|(?:medium))/)[1];

          $downloadButton = $('<a class="sc-button sc-button-download sc-button-icon sc-button-responsive">Download</a>').attr({
            title: "Download this sound (" + conversionHelper.bytesToMB(data.original_content_size) + ")",
            href: downloadUrl
          }).addClass("sc-button-" + size);

          $buttonGroup.append($downloadButton);
        };
      })($sound);

      $.getJSON("http://api.soundcloud.com/resolve.json", params).success(onSuccess);
    }
  }
})(window);

ARCHIVE PRE-2013 WORKING VERSION for Firefox bookmarklet:

javascript:(function(a){var%20b=a.createElement("a"),c=a.createElement("span"),d=a.querySelector("#main-content-inner%20img[class=waveform]").src.match(/.com/(.+)_/)[1],e=a.querySelector("em").innerText+".mp3";c.innerText="Download",b.appendChild(c),b.setAttribute("class","pl-button"),b.setAttribute("style","background-image:%20url(http://soundcloud.com/images/icons_mini.png?unicorn26);%20background-repeat:%20no-repeat;%20padding-left:%2018px;%20background-position:%20-77px%20-236px;"),b.download=e,a.querySelector(".primary").appendChild(b),b.href="http://media.soundcloud.com/stream/"+d})(document);

Note the bookmarklet should be a single line:

javascript:[INSERT sc-dl-min.js];

Notice the semicolon at the end. The code works as of 24 Jan 2013.