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To explains them more clearly is your mesh's edges have to be fair and square.
It happens when mesh don't have well smooth edges.I don't see all the whole edges in your model.
If you can provide me some screenshot with edges display before subdivision I can tell you what to do to fix this.
I know sometimes i can fix some of objects by doing ctr+r and moving this purple circle close to the edge after setting subdivision and surface
I beleive I got what's wrong with you ,Have you ever tried to use Edge Crase ? incrasing those value would fixed those problem.
Have a look at this pages may help you understand better with Blender.
http://blender.stackexchange.com/questions/6425/keep-sharp-edges-when-using-subdivision-surface
https://www.blender.org/manual/modeling/modifiers/generate/subsurf.html
Would take sometime but I hope you read it and your problems would be solved.
You have several things that don't look right, hopefully something below will help you out.
For the base, assuming you want a flat disc with nice edges. Take a look at this image :
https://www.dropbox.com/s/2etp38q1hkct8t4/Mesh_example.png?dl=0
This is set to the same Sub-D level as your disc(1). You really should have it set to at least 2 for the render(also when you are modelling it so you can see what it will look like).
I tend to work at a Sub-D level of 3 when modelling an object, then knock this down to 1 or 2 when working on other parts.
I have enough support loops on my mesh. You tend to need 2 if you want the shading to be correct, if you recreate this with only one support loop on the top of the disc you will see a slight inaccuracy.
I just used "i" to inset twice on both the top and bottom faces of the cylinder object(you will need to enable "Inset Polygon" in the Add-On's under User Prefs for this to work. This is essential for HS(Hard Surface - Sub-D) modelling, you can flip it to Outset as well as inset. You need to enable the “Loop Tools” add-on as well(if you have not already done so) for being able to do this type of modelling effectively). For the outer edge I just added 2 loop cuts (“Ctrl+r” and mouse wheel up 1)
You can see in the final object that the shading is set to smooth for the entire object, you don't seem to be doing this on a lot of your mesh objects so they are going to look wrong. For Sub-D modelling the object's shading should always be set to smooth!
I'm guessing when you do do this it looks really messed up in places(like your mesh does in the 3rd example). Again this is because you have not modelled with support loops.
You can use Edge Crease as @Zenogias has said, but this is considered by many as a quick rough fix for use on background objects only. I sometimes find it can have occasional uses beyond this but not often.
Depending upon the mesh(model) you are trying to create it can be utterly useless at times as it will create artefacts that are visibly noticeable and unfixable via this shortcut method.
You are best off learning how to use support loops properly, especially if you have any interest in doing this professionally at some time if the future.
Couple of other quick points :
When working on very rounded surfaces(say trying to create rivets on a helmet) you will need a dense enough base mesh to cut the detail into, if you don't then the outlining geometry will be affected by the detail geometry and you mesh will show deformities(artefacts) in many places.
For circles and spheres having a lot of verts in you base mesh can cause this sort of artifact :
https://www.dropbox.com/s/j3fywx7inbsxb1e/Mesh_example_2.png?dl=0
You will see the one with less segments has a much less noticeable artefact in the middle than the one with 32. So sometimes more verts is bad when using Sub-D.
Also check out the Hard Surface modelling tutorials in this list here :
http://steamcommunity.com/app/365670/discussions/0/541906348054659940/
A guy called Master Xeon has made an add-on called “Hard-Ops”, I think it is available for around £5 ish. I'm tempted to pick this up at some point in the future as it looks pretty quick and powerful for many Hard Surface modelling situations... He posts on the Artwork section a lot and is on Youtube as well.
What I've been doing with really stubborn objects lately is If I need to round a surface and have sharp edges as well, I'll split the mesh I want to work with out into its own object. Then I'll add a Subdivision Sub Surface modifier (lvl 2 or 3) and add an edge split modifier to the stack.
After working the piece and before I join it back onto the original object I split it away from, I'll knock the subsurf back to that of the original (to see if I can get away with it), If I can, I delete the subsurf then apply the edge split to retain the mesh. If I need to retain the mesh from the subsurf, I'll bump it to the minimum level I can and apply that as well (before I apply the edge split)