One feature I always use, be it on the desktop, servers or my phone is the search. I search for documents, files and even grep within those results on desktop and some times on the servers. On the phone, I search for emails, contacts and notes. Yes search makes my life easier and Google Android team has come out with QSB, Quick Search Box that makes it even easier on Android Phones.
The QSB will search content on your phone, including apps, contacts, and browser history, as well as content from the web, like personalized search suggestions, local business listings, stock quotes, weather, and flight status, all without opening the browser. QSB even learns from your habits and provides faster access to the items you search for and use most often (by, for example, moving them higher on the suggestions list).
Yes my thumb will be hitting this feature, very, very often
Official Google Mobile Blog: Quick Search Box for Android: Search your phone and the web