The Android version of Google Play Books got this feature about a month ago. It's intended to help readers make better use of the texts that Google has scanned and uploaded as part of the Google Books project (the one that was recently found to be fair use).
And just to be clear, it doesn't technically let you search the images of pages of books; instead readers get to search the text files that Google created after the volumes were scanned. On Android it looks something like this:
This feature is probably going to be a boon to researchers as well as anyone who reads the old books found in Google Books; let's just hope that no one falls victim to the mysteriously deleting ebooks bug which one historian discovered earlier this year.
You can find the app in iTunes.