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I'm just getting started at Blender - so far I've been making stuff by subdividing and extruding vertices, and then filling in the faces.

Unfortunately, when I load up these models, individual faces go missing:

gif of the problem in action

If it matters, I'm using the OBJ file format.

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    $\begingroup$ With all the vertices of your mesh selected in edit mode, press T to open up the Tool Shelf and under the Shading/UVs tab, click Recalculate to recompute the proper direction of all your faces. However, I notice that you seem to have some faces that are just standing out on the model by themselves, and this can be a dangerous practice so I would recommend avoiding that. I'm not sure what you mean by "using the OBJ file format", but I would stick to saving your models as blend files unless you're exporting them to other programs. $\endgroup$
    – CGEffex
    Commented May 2, 2017 at 18:12
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    $\begingroup$ Yes internal faces are discouraged and a bad practice, and most likely the source of your problems. Try to keep the mesh consistent and manifold, and avoid internal faces. The rue is one edge should only always belong to two faces, no more. $\endgroup$ Commented May 2, 2017 at 18:14
  • $\begingroup$ It's supposed to look like this - two faces per edge, always. @DuarteFarrajotaRamos $\endgroup$ Commented May 2, 2017 at 18:19
  • $\begingroup$ @LukeD added... $\endgroup$ Commented May 2, 2017 at 18:48

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What you have:

yours

Internal faces (pointed by Duarte Farrajota Ramos), loose edges, unconnected vertices, unnecessary faces...

You can try to clean it up by Recalculate Normals (suggested by CGEffex), Remove Doubles, cutting faces and connecting vertices to have mostly quad topology.

You should avoid creating ngons and tris (these could be useful sometimes).

But...

What you need:

need

In this particular case you can recreate this mesh fairly easy just by using Extrude and Snapping (to existing mesh).

I will not explain it step by step as this is kind a Blender 101 and you can find large number of tutorials about extruding basic shapes.

Final thoughts:

You have mentioned that you are using .OBJ files. I understand that you are importing them. If yes then it will not be easy to clean them up. I have fairly good experience with them (exported from various CAD-like software) and always it was nightmare to work with. I can't give you any more tips besides those from above. In my case I've recreated from scratch 70-80% of meshes just to save some time.

Blend file:

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