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There have been many studies done into this, and a lot of folks offer different opinions!. One noteable test one was done on TV by Mythbusters. While they found the difference as to 'with' or 'without' a tailgate to be small, they found that it is better to have the tailgate up rather than down/removed.
Personally, I split the difference and installed a CustomFlow louvered 'V' tailgate and it is on the truck all year. I cannot tell any difference in the fuel mileage I have with this tailgate and that which I got before I bought it. I like the usefulness of the V-gate, as I no longer have to drop the gate to hitch or unhitch. I tried for a time not having a tailgate on at all - bad choice, as stuff fell out of the back!

This is what MythBusters reported:
Tailgate: Up or down?
Myth: Driving your pickup with the tailgate down gives you better fuel efficiency than with the tailgate up.
Update: Tailgate Up or Down Revisited
Test Setup
Adam and Jamie were each given identical, new model pickup trucks. They both had equal mileage, same tire pressure, and 30 gallons of gas. Jamie drove with the tailgate up and Adam the tailgate down.
The rules:
They have to maintain the speed limit
All acceleration must be done by cruise control
No drafting
Windows up, A/C must be exactly the same in both cars
The Test
After 300 miles there didn't appear to be much difference in the gas consumed, but after 500 miles Adam (tailgate down) ran out of gas. Jamie made it another 30 miles before he ran out of gas. This result was the exact opposite of the myth.
Water tunnel visualization
According to the experts, a circular pillow of air forms behind the cab of the truck when the tailgate is up. This "separated bubble"/"locked vortex flow" keep the faster moving air from contacting the truck, and thus reduces drag. With the tailgate down, the bubble breaks down and is no longer able to keep the fast moving air out, increasing drag.
In their scale model with the water tunnel, they were able to see that the increased drag. With the tailgate down, the particles in the water were dropping down and hitting the tailgate.
mythbusted