Say no to Chrome!
What Goes to Google
Google's full list of privacy notices about Chrome, and what its browser sends back home, is a very public document. Here are some highlights, and explanation:
Searches, or partial searches, for auto-complete suggestions: Almost entirely so that Google can throw you back some relevant results. You can disable this in Chrome's "Under the Hood" settings by un-checking the "Use a prediction service" setting.
Searches or URL loads with Instant enabled: If you've enabled Instant in your settings, or from the about:flags section, it's safe to presume that pretty much every character you type into Chrome's address bar is sent, analyzed, and returned to you. Instant searching is not enabled by default.
Full size
"No such page" results on some sites: If a site doesn't have its own 404/"Sorry, this page doesn't exist" that's semi-substantial, Chrome may offer its own "Maybe you meant this" page, according to Matt Cutts. You can disable this in Chrome's "Under the Hood" settings by un-checking the "Use a web service to help resolve navigation errors" setting.
Bookmarks and other sync data: Like your Gmail, Docs, and other personal effects, Google keeps the data you want synced between browsers on its own servers, but promises to be a "responsible steward" of that data, as outlined in their general privacy policy.
Crash reports and usage statistics, if enabled: