Starting around mid-May, using Google with the Opera browser was somewhat of a challenge. In short, if you went to Google.com, entered a keyword search and hit the return key, Google would not do anything. You had to manually click on the "Google Search" button with your mouse.
A Google Web Search Help thread has dozens of reports from unhappy Google and Opera users. Google confirmed the bug on June 1st, saying:
A fix is on the way!
Pretty soon, hitting the Enter key after typing a query will perform a Google search in the versions of the Opera browser that you've reported.
I wanted to check in with all the relevant people on my team before giving you the official word on this issue. That explains the delay in my response. I understand the frustration at not hearing sooner about such an important issue. Promise to do better next time (lets hope there won't be a next time!).
Currently, it appears the enter key now works on the search results pages, but searching in Google.com's home page, still requires the click of a mouse.
I believe the bug came with Google's new Google suggest features which launched on the same day the bugs began being reporting.
Forum discussion at Google Web Search Help.