I don't know about the technical details of the implementation of those other sites. However, if there are sites that don't use account or cookie prefs to know what you normally search, I would expect nothing less than different results.
Google has been personalizing search results for years to give you information tailored to your needs. Recently, Google search results have been more explicit, displaying search results based on what people in your friend network work have shared. Also, see ratings and reviews on Google Places, for example, where your ratings and those of your friends modify your results giving you better, more personalized information.
Author's note (July 2016): The answer below was written in 2011, and is still working in Google Search. I have published new extensions that use a different method to remove the search result indirection, which works on even more Google sites and on mobile.
TL;DR: Don't track me Google is a user script Don't track me Google is an extension I made that allows you to copy normal URLs, while hiding the referrer to the sites you're visiting.
Installation
Explanation
I have written a method which replaces the link-modifying rwt function with a bogus function that can't be touched by Google.
By preventing Google from overwriting the rwt function, the link cannot be modified any more. This method depends on the Object.defineProperty method (Firefox 4+ and Chrome 5+). The fallback requires Firefox 2+ and Chrome 1+.
Firefox 2+
If you only want to remove the link-modifying behaviour, and not care about showing your search queries through the referrer, this GreaseMonkey script can be used:
(very non-strict @include rules using wildcards and the Magic TLD)
// ==UserScript==
// @name Don't track me Google
// @namespace Rob W
// @include http://*.google.tld/*
// @include https://*.google.tld/*
// @version 1.2
// @grant none
// ==/UserScript==
"use strict";
if (Object.defineProperty) {
Object.defineProperty(unsafeWindow,"rwt", {value: function(){return !0;}, writable: false });
} else {
unsafeWindow.__defineGetter__('rwt',function(){return function(){return !0}});
}
Google Chrome does not support Magic TLDs, so the closest you can get is *://*.google.com/* (repeat the rule, replace .com with other supported Google TLDs).
In Chrome, scripts have to be injected in the form of a <script> tag, because Content scripts are executed in an "isolated world".
Chrome & Firefox 2+ - Link to source code
On January 21st, 2012, I published an extended version, which includes a referrer-hiding method, so that others cannot see your search query. This greatly improves your privacy.
(Update from 2016: this referrer hiding is not needed any more in modern browser because of the referrer policy, which only shows the domain in the Referer header)
Best Answer
One of the reasons is so they can do click tracking on what link you clicked, on their search results page. This allows them to detect and optimize their search results.
For example if they noticed everyone that searches for "batman" only ever selects the 2, 3, 6, 7 links, they could remove the 1, 4, 5 links as they are obviously bad results for this search word.
Also you should take a look at Google's search history. I can tell you are logged in from this link and that your search history is being logged. This will give you a good indication of the information that Google collects when you click this link.