No they don’t!
I was at a trade show yesterday showing everyone my great visibility on Google Canada for the term “emarketing” and someone visiting my booth asked: “Is that visibility because we are in Montreal and your marketing business is located in Montreal?” and it was a great question.
So my kids (I have 6) in Ottawa, Tortonto and Vancouver did the same search and they all got the exact same results but the mix of sites on page one was slightly different in each case.
However, for local searches in your city, people a few kilometers away from you doing the same search will in fact see different results because businesses that are local to their location will show up before the local businesses near your location. As in everything to do with Google, there are always exceptions but, local search is really becoming localized.