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I am new to Blender, and am currently following tutorials to try and generate a rig using rigify. However as you can see, it's only generating a rig for a few bones, not the complete skeleton: 
After searching for a solution, the only answer I can find is to make sure Auto Run Python Scripts is turned on, which it is. Here (hopefully, if I've done it right!) is my Blender file:
Rigify uses a python script to generate the controller rig. Changes to the base metarig can mess up this script, preventing parts of the armature being generated.
While it looks like you started with the metarig, your rig doesn't have a spine or shoulder bones. The original metarig has hips-spine-chest-shoulder-upper_arm you have hips-chest-upper_arm. These missing bones will be the reason the script is failing.
Create a new metarig and adjust the existing bone positions to where you want them, leaving each existing bone in place.
I've got the same problem. In my case the rig generated the root only. I've found that the reason was the fact that I changed the name of the rig from "metarig" to "rig". CHANGING THE NAME back to "metarig" solved the problem.
