Tumblr only allows a maximum width of 500px for embedded YouTube videos. Paste this script into your theme, change contentWidth and the embed code will be updated accordingly.

gistfile1.html

  <!-- Widescreen YouTube Embeds by Matthew Buchanan & Hayden Hunter
  http://matthewbuchanan.name/451892574
  http://blog.haydenhunter.me
  
  Hacked around by Simon Starr to break out of Tumblr's max width of 500px
  http://www.simonstarr.com

  Original source here: http://pastie.org/871790

  Released under a Creative Commons attribution license:
  http://creativecommons.org/licenses/by/3.0/nz/ -->

  <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
  <script type="text/javascript">
  $(function() {
    // Change this to whatever width you like
    var contentWidth = 700;
    
    $("object").each(function () {
      if ($(this).find("embed[src^='http://www.youtube.com']").length > 0) {
        // Identify and hide embed(s)
        var parent = $(this).parent();
        parent.css("visibility","hidden");
        var youtubeCode = parent.html();
        var params = "";
        if (youtubeCode.toLowerCase().indexOf("<param") == -1) {
          // IE doesn't return params with html(), so…
          $("param", this).each(function () {
            params += $(this).get(0).outerHTML;
          });
        }
        // Set colours in control bar to match page background
        var oldOpts = /rel=0/g;
        var newOpts = "rel=0&amp;color1=0xeeeeee&amp;color2=0xeeeeee;hd=1";
        youtubeCode = youtubeCode.replace(oldOpts, newOpts);
        if (params != "") {
          params = params.replace(oldOpts, newOpts);
          youtubeCode = youtubeCode.replace(/<embed/i, params + "<embed");
        }
        // Extract YouTube ID and calculate ideal height
        var youtubeIDParam = $(this).find("embed").attr("src");
        var youtubeIDPattern = /\/v\/([0-9A-Za-z-_]*)/;
        var youtubeID = youtubeIDParam.match(youtubeIDPattern);
        var youtubeHeight = Math.floor(contentWidth * 0.75 + 25);
        var youtubeHeightWide = Math.floor(contentWidth * 0.5625 + 25);
        // Test for widescreen aspect ratio
        $.getJSON("http://gdata.youtube.com/feeds/api/videos/" + youtubeID[1] + "?v=2&alt=json-in-script&callback=?", function (data) {
          oldHeight = /height="?([0-9]*)"?/g;
          oldWidth = /width="?([0-9]*)"?/g;

          newWidth = 'width="' + contentWidth + '"';
          if (data.entry.media$group.yt$aspectRatio != null) {
            newHeight = 'height="' + youtubeHeightWide + '"';
          } else {
            newHeight = 'height="' + youtubeHeight + '"';
          }
          youtubeCode = youtubeCode.replace(oldHeight, newHeight);
          youtubeCode = youtubeCode.replace(oldWidth, newWidth);
          if (params != "") {
            params = params.replace(oldWidth, newWidth);
            params = params.replace(oldHeight, newHeight);
            youtubeCode = youtubeCode.replace(/<embed/i, params + "<embed");
          }
          // Replace YouTube embed with new code
          parent.html(youtubeCode).css("visibility","visible");
        });
      }
    });
  });
  </script>