Well, a lot of the things you can do with the API, you could do some other way, emulating manual requests, but its much more stable and easier using the API, because its designed to be queried by a program.
This is discussed several times here in DP. Try searching this forum. Here you will find some more info... http://forums.digitalpoint.com/showthread.php?t=2923 Remember there are several APIs provided by google, be clear about which API you are talking about.
Hi, It would give webmasters access to critical data such as top search queries or top search query clicks for any given domain.you can add more functionality to your Web applications than just what your own Ajax scripts and server-side programs provide.It shouldn't be hard to build on what you learn here and start utilizing the Google API with your Ajax apps. More importantly, though, you will have a pretty good idea of how to use public APIs in general including the one from Amazon, del.icio.us, or anywhere else.
Oh yes, you need to be clear about which APIs from Google you are talking about. So there are lots of them, from AJAX,XML,Search,maps etc.. It is like sitting on the shoulders of the Giant.
The benefit of the Google API is that it is an interface Google provides for querying its databases (and it allows people to query the server using scripts, which is otherwise prohibited by the Google TOS).