Last night I received an email from a pilot, whose friend flew a Gogo-equipped Boeing 767-200 from LAX to MIA. The pilot was able to log on to the Internet, go to the DUATS web site, and view the current NEXRAD radar map from present position (over Texas at the time) all the way to destination in near-real-time (NEXRAD updates about every 5 minutes).
This is exactly the type of weather product that could enhance safety of flight by being connected.
Airborne weather radar is limited to about 150 miles or so range at typical jet cruising altitudes, because of the curvature of the earth. By being able to view current radar downrange - as well as 24hr forecasts - longer-term planning for routing and weather avoidance is greatly enhanced.
Here's what some NEXRAD radar and satellite pictures look like. Now tell me this wouldn't be helpful in-flight.