What kind of mechanical engineering jobs are at Google Inc,?

I would also encourage you to check out some of our programs available for High School Students at this link: http://www.google.com/edu/programs/. It will help get you on the radar if you're interested in pursuing a career at Google down the line!

Obviously most of the engineers at Google are software engineers, but there are indeed a few opportunities for many other kinds of engineers. A few mechanical engineers can be working in data centers, and there might be a few special projects (such as those in Google[x]) which may occasionally need a mechanical engineer. Those who work in datacenters will occasionally travel to other datacenter sites, or to offices where datacenters are planned. I see a couple datacenter mechanical engineer postings which indicate an expectation of traveling 30% of the time. Here's a job search for Google jobs related to mechanical engineering:
https://www.google.com/about/careers/search#t=sq&q=j&d=mechanical&li=10&j=mechanical&
...and even if you are primarily a mechanical engineer, it will really help to get at least a bit of software engineering under your belt, too.

There are indeed opportunities at Google for mechanical engineers. In particular I was chatting with one of the people who leads a team of MEs at Google just last week--his team helps work on hardware devices like Chromebooks, Nexus phones and Chromecast. As Google designs and produces more hardware devices, the need for MEs is likely to grow. Good luck!