I've created a number of poses for my rigged character. These poses were created while he was at the center of the grid in the 3D viewer. When I apply a pose anywhere else, it places him back at that location. How can I use the poses I've created at any other locations than where they were created?
In most cases, your Armature object should be the root of object hierarchy. So that means it should not be parented to anything.
Also the armature object should be without any transforms - always with origin in the center.
Instead the rig should have a Root or Master bone to transform the whole rig in pose-mode. You want to make rig positioning in the scene with this bone.
This prevents numerous problems with scene management, linking, and most importantly keeps things clean for animators - they have all the key-frames under the pose. And not some under object and some under pose.
When you do not want to store the root transform of your rig inside a pose library - delete that bone from the Action which is used to store the poses - or just delete the keyframes from the poses you don't want to store the root transform in:
Should be named PoseLib by default and you will find it in Action Editor.
Make your Armature a child from an object, In that way, the poses are always relative to the parent-object.
To do this, first select all your children, in your case select the armature. With all children selected, finally select your parent-object (In your case a simple Empty-object or similar). Press Ctrl + P to parent all selected objects (children) to the last selected object (parent).
Note: Because the armature is now a child-object, always reset the transform of the parent-object, if you add or modify an animation, otherwise the results are not clean.
Tip: If you're using it in the BGE use a rectangular or capsule as the parent in the dimensions of the character. Set 'Physics Type' to Dynamic, Rigid Body, Character or what ever is best for your purpose and more importantly set to invisible.
I hope I could help.