What program to do effects like in this video?
 

Wonderful 3 minute video by National Geographic on global population:

YouTube - 7 Billion, National Geographic Magazine

They have some very nice text effects and basic animations. What would be the easiest to learn program to do equivalent or near equivalent text effects and similar animations? Any guidance would be appreciated.

You could do that with any motion graphics program. The odds are that it was made with After Effects, or maybe Flash. There are also elements that were probably made in Illustrator (line drawings & other graphic elements) or Photoshop (background textures) and then brought into AE of Flash to animate.

I have done stuff like that in AE and Motion. Text effects do feel more like AE though.

Hi Mathew. As mentioned any Motion Graphics program would be able to do it. The basic style is called 'Kinetic Typography', if you do a search you will find various tutorials which will give you a starting point on deciding on a program (though yes, it does feel like After Effects).