Aaron Wall has a nice write up on the different ways one searcher can see one set up results, compared to a different search seeing a different set up results, all for the same search query. Aaron explains that three primary things may determine the results sets you see for any particular query. They include the search engine data center you hit, the location of your computer and if you have personalization preference turned on.
Data Centers: Depending on the search engine, especially Google, you may hit a data center that has a different set of indexed pages or a slightly different algorithm. Both have an effect on the search results you see. Google has multiple data centers in order to help return you a quicker response and because it enables them to roll out different indexes and algorithms slowly and to select users. As you can imagine, it will affect the result sets you see.
Geographic Location: Some times, Google tailors the results to your location. So if you are in London, Google may show you results that are more relevant to a person in London. How? They may show more results from .co.uk domains, or from servers hosted in the area or sites that have the language.
Personalization: With most search engines now, you can now sign in, and enable personalization. That means the search engines look at your search history and other preferences and tailor the results specifically for you. As you can imagine, this will have an impact on the results you see for a particular query.
I did not really read Aaron's post, but I suspect it says the same thing I said above. If not, you can blast me in our forums. Read Aaron's post here, it is a nice topic.