Can Javascript read the source of any web page?

Simple way to start, try jQuery

$("#links").load("/Main_Page #jq-p-Getting-Started li");

More at jQuery Docs

Another way to do screen scraping in a much more structured way is to use YQL or Yahoo Query Language. It will return the scraped data structured as JSON or xml.
e.g.
Let’s scrape stackoverflow.com

select * from html where url="http://stackoverflow.com"

will give you a JSON array (I chose that option) like this

 "results": {
   "body": {
    "noscript": [
     {
      "div": {
       "id": "noscript-padding"
      }
     },
     {
      "div": {
       "id": "noscript-warning",
       "p": "Stack Overflow works best with JavaScript enabled"
      }
     }
    ],
    "div": [
     {
      "id": "notify-container"
     },
     {
      "div": [
       {
        "id": "header",
        "div": [
         {
          "id": "hlogo",
          "a": {
           "href": "https://stackoverflow.com/",
           "img": {
            "alt": "logo homepage",
            "height": "70",
            "src": "http://i.stackoverflow.com/Content/Img/stackoverflow-logo-250.png",
            "width": "250"
           }
……..

The beauty of this is that you can do projections and where clauses which ultimately gets you the scraped data structured and only the data what you need (much less bandwidth over the wire ultimately)
e.g

select * from html where url="http://stackoverflow.com" and
      xpath="//div/h3/a"

will get you

 "results": {
   "a": [
    {
     "href": "/questions/414690/iphone-simulator-port-for-windows-closed",
     "title": "Duplicate: Is any Windows simulator available to test iPhone application? as a hobbyist who cannot afford a mac, i set up a toolchain kit locally on cygwin to compile objecti … ",
     "content": "iphone\n                simulator port for windows [closed]"
    },
    {
     "href": "/questions/680867/how-to-redirect-the-web-page-in-flex-application",
     "title": "I have a button control ....i need another web page to be redirected while clicking that button .... how to do that ? Thanks ",
     "content": "How\n                to redirect the web page in flex application ?"
    },
…..

Now to get only the questions we do a

select title from html where url="http://stackoverflow.com" and
      xpath="//div/h3/a"

Note the title in projections

 "results": {
   "a": [
    {
     "title": "I don't want the function to be entered simultaneously by multiple threads, neither do I want it to be entered again when it has not returned yet. Is there any approach to achieve … "
    },
    {
     "title": "I'm certain I'm doing something really obviously stupid, but I've been trying to figure it out for a few hours now and nothing is jumping out at me. I'm using a ModelForm so I can … "
    },
    {
     "title": "when i am going through my project in IE only its showing errors A runtime error has occurred Do you wish to debug? Line 768 Error:Expected')' Is this is regarding any script er … "
    },
    {
     "title": "I have a java batch file consisting of 4 execution steps written for analyzing any Java application. In one of the steps, I'm adding few libs in classpath that are needed for my co … "
    },
    {
……

Once you write your query it generates a url for you

http://query.yahooapis.com/v1/public/yql?q=select%20title%20from%20html%20where%20url%3D%22http%3A%2F%2Fstackoverflow.com%22%20and%0A%20%20%20%20%20%20xpath%3D’%2F%2Fdiv%2Fh3%2Fa’%0A%20%20%20%20&format=json&callback=cbfunc

in our case.

So ultimately you end up doing something like this

var titleList = $.getJSON(theAboveUrl);

and play with it.

Beautiful, isn’t it?