Active artboard should correspond to the focus of the mouse or object(s) last placed on it.
The active artboard should either be activated by the position of the mouse, or from the placement of the last object. For example, using the mouse, I move an object from one artboard to an adjacent one. Therefore, the active artboard should be the adjacent one since I just placed an object on it. The reason this important for me is when I want to place this object on a new artboard and immediately center it to the page. However unless, I click on this new artboard first to activate it, Illustrator still has the previous artboard as active, and the object gets centered on it instead of the new one.

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Yes, I agree. I learned to make an actual click to focus the artboard, but I’d prefer not to.
However, I always remember things like this should come only as an option, because workflows differ, and there are certainly many users who would like the way it works today (and even if we can’t comprehend why).There are at least two related requests:
1. Make an option to disable auto-selection of artboards, when clicked inside — http://illustrator.uservoice.com/forums/333657/suggestions/36489226 (23 votes currently)
2. Artboard instant activation by mouse hover — http://illustrator.uservoice.com/forums/333657/suggestions/48810737 (just two votes)...and why not mention this bug:
Dragging a new guide from a rule activates the artboard behind the ruler
http://illustrator.uservoice.com/forums/601447/suggestions/34593415