What makes you trust Opera any more already? They're already quite capable of logging every domain you visit, via the fraud prevention mechanism (Enabled by default). Whether Opera are recording this I don't know, but you can probably be quite certain that Facebook will, if they acquire it.
That's exactly the fear – Opera doesn't have much reason to link recorded data back to you, facebook does, and is known to permanently store all available data. And it already knows way too much about you.
Correct me if I'm wrong, but isn't that a Google Search thing, not a Chrome thing? The Google toolbar in Firefox had the option to upload your browser's entire history to the Search History site, but that's not built into Chrome, afaik.
Chrome does have a sync service, but it requires user action to activate, allows the user to pick what they want synced, and allows syncing omnibox history, not the complete browser history.
