I was a contractor for about a year at Google in 2010. I had similar experiences to the other respondents, saw peers convert from contractor to full-time employee, but I did not. I had every opportunity to apply for jobs internally, but didn't find something while I was there.

Having Google on your resume will open doors and advance your career. I wouldn't have made as much progress in such a short period of time had I stayed on after my contract ended. Three years later, I've been hired by Google as a full-time employee, armed with real-world experience from a startup and perspective that is often lacking at in the highly sheltered confines of Big G. Had it not been for the contacts I made during my contract job, I'd not be working at Google today.

To sum: Google isn't making a long term investment in you as a contractor, so you'll be locked out of the real valuable perks. You'll benefit from the contacts and experience, so it's absolutely worth doing. Googlers are generally concerned for their colleagues, contractors included, so you have a good shot at being hired after your contract. Work hard, earn respect, keep in touch with your Google colleagues, and look out for the right job.