Ruby, 155 186 195 148 138 110 97 characters

require'open-uri';puts open('http://codegolf.stackexchange.com/posts/28159/body').read[/req.+;/];

I had to make it one line, because otherwise it would output newlines as \n instead of actual newlines.

• +31 characters because I didn't notice some characters were being escaped.
• +9 characters to get rid of the annoying backslash.
• Thanks to Nathan Osman for saving 2 chars, and Ventero for saving 55 (!!!) by removing the need for most of the fixes listed above.

The explanation

Let's beautify this a bit first. However, I'm going to have to use a somewhat... interesting notation in this code. I can't use semicolons at all in this post, for reasons explained later, so I will use {SEMI} in place of semicolons instead.

require 'open-uri'
resp = open('http://codegolf.stackexchange.com/posts/28159/body').read
puts resp.match(/req.+{SEMI}/){SEMI}

Alright, now let's walk through this. The first two lines are fairly self-explanatory -- they fetch the HTML text of this answer.

Now, the last line is the interesting one here. You see that seemingly useless semicolon at the end of the code? It's absolutely required, and here's why.

First, resp.match extracts the code to be printed. The regexp it uses for this is the trick: /req.+{SEMI}/. It grabs the start of the code, REQuire'net/http', by searching for req (re would grab my REputation). Then, it finds the end of the code by searching for a semicolon! Since + is greedy by default, it will keep going until it finds the semicolon that signifies the end of the code. See why I can't use semicolons anymore?

After that, I don't have to unescape anything thanks to Ventero's fix of not using \ at all anymore. All I have to do is fix {AMPERSAND} changing into {AMPERSAND}amp{SEMI}, which can be achieved simply by removing the amp{SEMI} part. No need for this anymore because of new URL. After that, the original code has been retrieved! (Note: I can't use the ampersand either, because that gets HTML-encoded which causes a semicolon to be created.)

Bash + coreutils + Lynx browser, 61 bytes

Thanks to @FDinoff for the tips:

lynx -dump codegolf.stackexchange.com/posts/28164/body|grep 2

JavaScript - 123 122 101 95 92 91 87

with(new XMLHttpRequest)send(open(0,'/posts/28175/body',0)),alert(/w.*/.exec(response))

Runs in the console of your web browser on this page. Tested on the latest Chrome and Firefox.

Ruby + wget + gunzip, 159 86 82 71

Using tip of @FDinoff to use http://codegolf.stackexchange.com/posts/28173/body.

puts `wget -qO- codegolf.stackexchange.com/posts/28173/body`[/pu.*\]/]

Tested. Thanks to @ace and @Bob for command line optimization.

Rebmu, 91 characters

Due to the Catch-22 I have to post to get this answer's URL. :-/ Okay, got it.

paTSrd http://codegolf.stackexchange.com/a/28154[th<a name="28154">th<code>cpCto</code>]prC

Rebmu is a dialect of Rebol, and you can read all 'bout it. The equivalent Rebol here would be:

parse to-string read http://codegolf.stackexchange.com/a/28154 [
    thru <a name="28154">
    thru <code>
    copy c to </code>
]
print c

Rebol's PARSE is a sort of highly-literate answer to RegEx. It starts a parser position of the input (which can be any series, including structural blocks...binary data...or string types). The rules are a language for how the parse position moves.

Tags and URLs are really just strings under the hood in the language. But they are "flavored", and as Rebol is dynamically typed you can check that type. READ for instance knows that if you give it a URL-flavored string, then it should dispatch to a scheme handler to do the reading. (In this case, the one registered for HTTP). You get back UTF-8 bytes by default, so we use to-string to decode that and get a series of codepoints in a normal Unicode string.

In the case of the parse dialect, encountering a tag type is just matched as if it were a string that looked like the tag. THRU is an instruction meaning "skip until the ensuing rule is matched, and then place the match position at the end of what you just matched." (TO is the analogue that matches, but leaves the parse position before the element).

So we zip along past the <a name="28154">. Then we zip past the next occurrence of <code>, with our parse position now located right after the >. PARSE's COPY command then lets us copy data up to another rule, in this case that rule is [TO </code>]... so we get into the variable C everything up until right before that <.

Cool, huh? :-)

Technically I could shave more off it, for instance by seeking TO "</" and that saves three characters--there's no need to match the whole </code> end tag when just </ would do. Similar arguments could me made for the start tag. But Rebmu is about literate golfing...even if you might think it looks odd at first!

CJam - 53

"codegolf.stackexchange.com/posts/28184/body"g54/1=);

I'm making this community wiki since I'm answering my own question and don't really want to compete :p
Credits to FDinoff for the URL choice.

Python, 175 bytes

This uses two external libraries; I didn't read that it was unauthorized.

import bs4, requests
print(bs4.BeautifulSoup(requests.get('http://codegolf.stackexchange.com/questions/28154').text).select('#answer-28171')[0].select('pre > code')[1].string)

Longer, but nicer looking code:

import bs4, requests
request = requests.get('http://codegolf.stackexchange.com/questions/28154')
soup = bs4.BeautifulSoup(request.text)
answer = soup.select('#answer-28171')[0]
code = answer.select('pre > code')[0].string
print(code)

Java 852, was 1004

Golfed: now replaces &gt with >

//bacchus
package golf;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.MalformedURLException;
import java.net.URL;
import java.net.URLConnection;
public class G{
public static void main(String[] args) throws IOException {
URL u;
URLConnection c;
InputStream i;
InputStreamReader r;
BufferedReader b;
String s;
int x=0;
try {
u=new URL("http://codegolf.stackexchange.com/questions/28154/write-a-program-that-downloads-itself");
c=u.openConnection();
i=c.getInputStream();
r=new InputStreamReader(i);
b=new BufferedReader(r);
while((s=b.readLine())!=null)
{
if(s.contains("//bacchus")) x++;
if(s.contains(">")){
s=s.replace(">", ">");
}
if(x>0)System.out.println(s);
if(x>2) break;
}
i.close();
b.close();
} catch (MalformedURLException ex) {
}
}
}
//bacchus

Submitting for testing, I will edit and try golfing it shortly. Needed to change x>1 to x>2 because test string is also in my code. Note: Code golf replaces > symbol to &gt.

//bacchus
package golf;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.MalformedURLException;
import java.net.URL;
import java.net.URLConnection;

public class Golf {

    public static void main(String[] args) throws IOException {
        URL u;
        URLConnection c;
        InputStream i;
        InputStreamReader r;
        BufferedReader b;
        String s;
        int x=0;
        try {
            u=new URL("http://codegolf.stackexchange.com/questions/28154/write-a-program-that-downloads-itself");
            c=u.openConnection();
            i=c.getInputStream();
            r=new InputStreamReader(i);
            b=new BufferedReader(r);
            while((s=b.readLine())!=null)
            {
                if(s.contains("//bacchus")) x++;
                if(x>0)System.out.println(s);
                if(x>2) break;
            }
            i.close();
            b.close();
        } catch (MalformedURLException ex) {

        }
    }

}
//bacchus

JavaScript, 200

r=new XMLHttpRequest()
r.open('GET','/posts/28157/body')
r.onreadystatechange=function(){if(this.readyState==4)alert((a=r.responseText).substr(i=a.indexOf(c='code')+5,a.indexOf('/'+c)-i-1))}
r.send()

Runs on this page.

Java, 300

//jules
import java.net.*;import java.util.*;public class G{public static void main(String[]a)throws Exception{Scanner s=new Scanner(new URL("http://codegolf.stackexchange.com/a/28189").openConnection ().getInputStream ()).useDelimiter ("//[j]ules");s.next ();System.out.print (s.next ());}}
//jules

An improved version of bacchusbeale's answer which:

• doesn't close resources unnecessarily
• doesn't declare unnecessary variables
• uses a Scanner to avoid having to loop over the input
• uses a regexp that doesn't match itself to avoid having to skip over a middle occurrence of the start/end marker.

curl -sL http://codegolf.stackexchange.com/q/28154 |awk -F\> '/\#/ {print $3}'

78 chars

Haskell, 563 613 bytes

import Control.Monad
import Data.List
import Network.HTTP
m%f=join(fmap f m)
q s=(simpleHTTP(getRequest"http://codegolf.stackexchange.com/questions/28154/write-a-program-that-downloads-itself?answertab=oldest#tab-top"))%getResponseBody%(putStrLn.head.filter((==)(s++show s)).map(take 613).tails)
main=q"import Control.Monad\nimport Data.List\nimport Network.HTTP\nm%f=join(fmap f m)\nq s=(simpleHTTP(getRequest\"http://codegolf.stackexchange.com/questions/28154/write-a-program-that-downloads-itself?answertab=oldest#tab-top\"))%getResponseBody%(putStrLn.head.filter((==)(s++show s)).map(take 613).tails)\nmain=q"

Tested. Has page support via "oldest posts" feature. Uses quine-line structure to find what to print. The import Control.Monad is only because >>= generates > in HTML.

Javascript, 138

a=window.open("http://codegolf.stackexchange.com/posts/28160/body");setTimeout('alert(a.document.body.innerHTML.match(/a=.*9\\)/)[0])',99)

This works assuming that the page loads in under 99 ms. It also has to be run via a console opened on a codegolf.SE page, because of the same origin policy.

Ruby, 237

require 'open-uri';require 'htmlentities';open ('http://codegolf.stackexchange.com/a/28159') {|f| f.each{|l| b = '' if l =~ /<c(.*)'htmlentities'/;puts HTMLEntities.new.decode l.gsub(/<\/?[^>]+>/, '') if b;break if l =~ /<\/code>/ && b}}