Google just updated its iOS Google Search app (iTunes link). I have always preferred searching for Web content on the iPhone using Google's dedicated search app, compared to the search box built in to Safari. Now the experience is better.
The updated app focuses on speed -- both in terms of how quickly it runs (faster, especially autocomplete) and with a few user interface tweaks that make using it feel a lot better. On a mobile device, like my underpowered iPhone 4, these little things matter. For example, if you're viewing a page you got to from the search app (it has its own browser), swiping your finger left to right on the page pops you back in to your search result list. It makes sorting through results much less of a chore.
There's a nice easy feature to search within a page, something that's buried in Safari.
The image search in the new app is also much faster, kind of magically so. On the iPad, scrolling among image results gives you a slick Coverflow-like animation.
The app doesn't have the greatest feature of the original Google Search app, where you could lift the phone to your face to activate the voice search option. Voice search is still there, but you have to press a button to activate it. Correction: This feature can be turned on in settings. (Likewise for Google Goggles, which is a really cool feature on a mobile device.)
Overall, a welcome improvement to the Google app. See the Google blog post announcing the change.