A common complaint across SharePoint installations is that users can never find the right document with SharePoint search. One quick, easy and incredibly cheap way to improve the results of your search engine is the increase the size of your search box.
People instinctively type more words into larger search boxes. The more words typed into a search query the better the results will be.
Although users can type unlimited characters into the box, they instinctively stop typing when they reach the far right of the visible area of the box. So instead of searching for "Status report for Logistics Department Auckland March 2013" people end up typing "Status Report Auckland" and complain that the search engine doesn't work.
Microsoft encouraged this hamstringing of search by providing a miniature search box on the default template. The default search box in SharePoint 2007 installations was tiny, it got bigger in SharePoint 2010, but I was aghast to see it even smaller in SharePoint 2013.
When will the horrors end.
The good news is that it is very easy to improve the size of your search box. It will be easiest if you include a large search box as a requirement for your designer before they give you their mockups or provide the CSS.
So how big should your SharePoint search box be?
The best place to look for ideas for search on your intranet is not from other companies intranets, but on the internet itself. Sites like Google, Amazon and eBay hire teams of usability experts to determine the most effective way to present search on their sites. You may not be able to hire these experts to help with your intranet, but you can make inferences about what their research is telling them by viewing their websites.
Amazon's search box, for example, will stretch to over half of the page width, while in October 2009 Google doubled the size of their search box and take from this observation what you will, Bing's search box is considerably smaller than Google's.
With this in mind I would make your search box as wide as you can. I would go for the whole page width, excluding your logo in the top left corner.