I believe Google is interested in autonomous cars because it fits with the one thing already do well... advertising.
The lion's share of Google's profit come from advertising, but where is the one place where people
It's also no secret that Google has been pursuing "personalized search results" as well as local search. What better vehicle (pun intended!) for these ads than an autonomous car. Autonomous cars would allow ads to be served based on exact location and destination. Advertisers would have a captive, ready to buy audience and since Google would know their destination, Google would also know their INTENT!!!
Google could show hyper-local, results for people searching their mobile device while they get a ride. Advertisers would love this because it would be highly targeted. Instead of someone hearing a radio ad for a business 50 miles away, someone could see or hear an ad (Google Music Anyone?) for a restaurant on the way to their destination. If Google could get enough buy in from advertisers they might be able to turn mobile internet into an ad supported medium like terrestrial radio or broadcast television!
But what if Google wants to take it further?
Autonomous cars themselves could flip the idea of ownership on it's head. A car that drives itself would have no reason to sit in the parking lot while you're at work or while you're sleeping, these are times when the car could be "working". Instead of owning a car, you would just hail one from the "Google Fleet" with your smart-phone.
Google's fleet of cars could have an internet connection, a large high resolution monitor, the exterior could be wrapped in advertising targeted to its driving area. The in-car entertainment could be ad driven. Browsing the web? Streaming music? Watching a movie? What's to stop Google from throwing advertising into the mix? These "intrusions" would be a small price to pay for a cheap "subsidized" ride. If Google could get the cost cheaper than a car payment, cab ride, or rental car people would certainly buy in.
Of course there are other reasons why Google could be into autonomous cars. It could help with their street-view program as cars could run 24/7 and they wouldn't have to pay people to drive around.
They could license the autonomous technology to car manufacturers or maybe they think that the aging Baby Boomers won't want to give up "driving" and this could fill the gap.
It will be interesting to see what road Google takes with autonomous cars.