I can see two broad patterns as far as the design of the search field is concerned. One like we see on Google has a button that the user can hit to initiate Search. (They could also hit enter to do so)
The other pattern much like what is on this site (stackexchange) do not have a button. So the only way the user can initiate search is by hitting enter.
Has anyone done any research or analysis of this pattern ? What I have noticed is that search fields without the explicit search button (that normally is a magnifying glass) have "Search" as placeholder text, left aligned, whereas when there is no button the placeholder is usually a "Magnifying glass icon" with "Search" all left aligned.