I use Google for web search, RSS feeds, email, calendar, and notes - to name a few. Independently, I search each application for relevant results.
If I'm logged in to my Google account for standard web search, why can't I see results from all of my Google apps? I shouldn't have to switch to each separate application in order to conduct a search.
I can imagine the Google standard web search (since I use this the most) showing breakdowns of each application, with relevant results underneath.
Included in this would be the extremely useful Search History for my own Google searches. Too often I'll be searching for something that I already searched for in the past.