Question: Is it possible to "pump" a powder the same way liquids can be pumped?

If so, what are the challenges? If not, what are some alternatives?

Answer: 
While pumping powders as a mix with swiftly moving gas is viable, one of frequently used alternatives for both powders and granular materials is [Archimedes' Screw](http://en.wikipedia.org/wiki/Archimedes%27_screw).

![enter image description here](https://i.stack.imgur.com/KE01J.gif)

Essentially, a helix in a diagonal pipe making the material "pour/roll" upwards the curve, allowing lifting it a long distance. This solution is frequently used in farming equipment for transporting grain or granulates. While it doesn't provide "pressure" for moving it through inert pipes, a "pipeline" of such screws can go a long way, and while it restricts transport angle, it provides a viable alternative especially for heavier materials where extreme air flows would be required to move them.
Yes you can pump powders using a diaphragm pump. The above comments all focus on alternate ways to transport powder they are not talking about pumping. Check out powder pumping with a diaphragm pump on youtube.