Is render time, openGL, or memory affected whether a modifier is applied or not? If I have an object looking exactly like I want it to using modifiers, is there any reason why I should "apply" the modifiers before rendering, or any other considerations? More specifically, is viewport speed, render time and/or memory affected by whether modifiers are applied or not?

My educated guess is that it takes less processing power to calculate and display an object with Array and Sub-D-Surf modifiers than it takes to display the same object with those modifiers applied because each individual face would have to be calculated as opposed to a lesser number of instances of the already calculated less complicated object as a whole. (Sorry, that's a mouthful of a sentence.)

I am making tires using various modifiers on just a sliver of the actual tire. Now that I am ready to duplicate it to four tires, I am wondering if I should duplicate the entire tire rig/hierarchy, including "emptys" for rotation objects, (or add another couple of array modifiers), or if I should "apply" it all, then duplicate the finished tire to four.

Thanks for your help!
-Ben
Viewport speed: The final displayed mesh is the same regardless of if you apply the modifier or not. Applying it will cost you the ability to have different settings for viewport and render for modifiers that do that, such as on the subsurf modifier.

Scene update (opening file, changing frames, etc): Applying bakes in the modifier, so it doesn't need to be calculated on updates anymore. So that's faster.

Render: modifiers "apply" on the fly when exporting meshes for render, so no  difference. Same output mesh is rendered either way. The modifiers have to all be updated during this process though, so applying will speed render startup a bit. 

So generally, not much performance reason to apply a modifier. The two main situations where you'd apply it are when you need to do something on the modifier output directly (like applying mirror modifier before rigging), or when a modifier is taking a long time to calculate and losing non-destructive editing of the modifier is preferable to waiting that out.