In 2010 Wikipedia moved their search box from the left of the page (directly below their navigation box), to the top right of the page. They posted a detailed explanation for doing so, including references to a number of research articles and results from their own research.
I'll quote some extracts, but recommend that you read the whole article:
Another factor that may have influenced user expectations is the
common placement of search engine features in the top right corner of
the web browser window. There are practical advantages of positioning
the search in the top right...
...several usability studies have pointed out a key advantage of
navigational elements being placed on the right: it gives immediate
access to the browser scrollbar. This is particularly valuable when a)
scrolling up and down a list of search results, b) scrolling up and
down an article you’ve just called up for information.
In addition, they were specifically interested in how the size of the search box influenced where it could be placed on the page.
The old search box is approximately 20 characters wide, the new search
box accommodates 24 characters. More importantly, due to the placement
of the old search box in the sidebar of the layout, widening the
search was impossible without either relocating it or widening the
sidebar.
The search box placement in the top right allows us to maintain a
fixed standard width from one page to the next, while giving us
maximum flexibility as to what that width should be.
As for non-English languages:
...we didn’t test the English Wikipedia against other languages which
had placed the search box directly below the logo, and we recognize
that this alternative placement is already an improvement to match
user expectations. However, based on the cited research above, as well
as the design reasons for moving the search box to the top right, we
still believe that the overall case for moving the search is
compelling even for those languages, if slightly less so.
Lastly, a summary:
In sum, we moved the search box to a) match web practices and user
expectations, b) make it possible to widen it consistent with common
usability recommendations, c) in response to actual observed problems
of test subjects when using the old search.
We also recognize that millions of Wikipedia users had adjusted to the
old placement, and will now have to re-adjust to the new placement.
However, Wikipedia’s global audience grows by tens of millions of
users every year (it is currently at 375 million unique visitors/month
world-wide), and we hope to grow it by hundreds of millions in this
decade. That will require that we adapt to common user expectations,
rather than expecting every new user to adapt to us. This will
unfortunately inconvenience those who have adapted to the old
placement. Do we absolutely know that to be the correct decision? No,
but the fact that existing users are temporarily inconvenienced by it
is not at all indicative that it is not.
Search is critical in Google's email since it ties in multiple services together
