Nearby objects won't move independently? I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside. 

I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces. 

Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it... 

I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated. 

Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.

I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand.
This is a guess, but it sounds like you might have Proportional editing (O) enabled.
See if it is enabled in 3D view &gt; Header:

Blender 2.7x: 

You can disable it by pressing O or clicking the icon in 3D view &gt; Header: 
Blender 2.7x: