The solution, for those of us who are slightly more civic minded than jliszka and don't want to crash any airplanes into the ocean, is a bit more complex. For convenience, I will assume that the total flight takes 24 hours.

0:00 - Planes 1, 2, and 3 depart, each with full tanks, heading west.
3:00 - All three airplanes 1/8 of the way around the world and at 3/4 tank. Airplane 3 tops off planes 1 & 2 and heads back to base.
6:00 - Plane 3 reaches base, refuels. Planes 1 & 2 both 1/4 of the way around the world and at 3/4 tank. Plane 2 transfers 1/4 tank to 1 and heads home. 1 continues.
12:00 - Plane 1 at halfway mark and 1/2 tank. Planes 2 & 3 launch with full tanks heading east.
16:00 - Plane 1 at 2/3 distance mark. Planes 2 & 3 at 5/6 point, each with 2/3 tank. Plane 3 transfers 1/3 tank to 2 and heads back to base. 2 continues.
18:00 - Planes 1 & 2 at 3/4 point. 1 is empty and 2 has 5/6 tank. Plane 2 transfers 5/12 tank to plane 1. Both head towards base.
20:00 - Plane 3 arrives at base, refuels, launches west. 1 & 2 at 5/6 point.
22:00 - All planes meet at 11/12 point. 1 & 2 have 1/12 tank. 3 has 5/6 tank. All three planes share equally, ending with 1/3 tank each. All fly home.
24:00 - All planes arrive to victorious ticker-tape parade with 1/6 tank of fuel to spare, and nobody had to make an emergency landing in Bhutan.
There is a second solution that avoids the nasty thirds, but it has all three planes coasting in on empty, which I'll avoid if I can help it ;)