I made a Python script that processes all Array Modifiers of an object but creates transformed objects rather than just the geometry. This solves a bigger set of this question's problem as using this script one can also keep the rotation and scale of the resulting parts (and join later). Have a look to this question where you'll also find the script:

How to obtain a set of separate objects from an Array Modifier (or other method) and keep their rotation and scale?

There are a few ways of accomplishing this without the use of the Array modifier that don't suffer from the separate parts issue.

Repeat last command shortcut

• In object mode press Shift+D to make a duplicate.
• Repeat using the Shift+R.
• Then select them all and preform the previous steps again in the other direction.

Dupli Object/Group

When using DupliVerts or (the more flexable) Particles. Not only do you have the option to easily make these real using Control+Shift+A. But can alternatively use a Group of objects and have them spread around in various ways.

1. Apply the modifier to make the data real
2. Enter edit mode on the object and press P > Separate by loose parts
3. Select all separated objects and press Shift+Ctrl+Alt+C > Origin to Geometry

This will make each piece an individual object with the origin located at the origin of the original object. Now you can manipulate them as you wish.

Note: Original object has to be one mesh. If original object consists from more parts (like Monkey head + 2eyes) you will have to connect them together by simple edge.

You can try to manually separate them in edit mode, and press P to separate By loose parts.

This won't work if your array element already has separate parts.