Two planes needed and three tanks of fuel.

Plane 1 and 2 start off together.  At the 1/4 mark in the flight around the world, plane 2 refuels plane 1 with half of its tank, and returns to the airport.  At this point, plane 1 has a full tank and can make it to the 3/4 mark around the world.  Plane 2 has just enough fuel to make it back to the airport.

When plane 1 reaches the halfway point around the world, plane 2 has reached the airport and can refuel and fly out again, in the opposite direction.

Plane 1 and 2 reach the 3/4 mark around the world at the same time (plane 2 only had to fly 1/4 of the way around the world since it flew in the opposite direction).  Plane 2 again refuels plane 1 with half of its tank, and both have just enough fuel to make it back to the airport.