Google launched a “Personalized Suggest” for Android, iPhone and Palm WebOS in US, that makes it easy to repeat your past searches. Just sign-in to the same Google Account on your computer and on your phone when searching, and select your search query from the list of search suggestions!. In addition, Web History needs to be enabled for your Google Account. Mobile users can turn on/off history by selecting "Save searches" or "Do not save searches" under Settings on google.com.