Do I have to notify anybody before flying a balloon?

In the United States, no there are generally no requirements to notify any authorities before launching an unmanned free high altitude balloon.  But there are some caveats.

By the FAA's definition, unmanned free balloons under 6 pounds per package, 12 pounds maximum load are exempt from reporting.  These do not require any form of waiver by the FAA to fly.  There are some other conditions that must also be met.

However, it is in everyone's best interest if the FAA is aware of your high altitude operation, so that aircraft and airports can be aware of the flight.  Notifying the FAA is a simple operation in which you would file a NOTAM (Notice to Airmen).  That NOTAM would be shared with local affected airports, and would also be available to pilots during their normal weather/safety briefings.  Some groups believe that the act of notifying the FAA of an operation would reduce the liability if there was a mid-air collision.  If you need assistance filing a NOTAM, there are nstructions on publishing a NOTAM.

From the community side, it is advised to announce your high altitude balloon flights to the Amateur Radio High Altitude Balloon (ARHAB) group by publishing the flights on arhab.org.