How does the way that I cut my garlic affect the taste of my food?
@Adam A is close -- it's not an issue of surface area on potency, it's an issue of damage to the garlic.  The 'strong' taste of garlic comes from a reaction as chemicals are released so they can mix (alliin and alliinase)

When you cook the garlic whole (as you would for roasted garlic), you will never get this reaction, as you'll break down the chemicals.  Also, the chemicals break down over long cooking, so even if you add a head of crushed garlic at the beginning of a batch of slow-cooked tomato sauce (4+ hrs), it's not going to have as strong a garlic flavor as adding a clove or two at the end.

One other way that the garlic prep can affect the taste is when you're sauteing, stir frying or other cooking over high heat -- larger bits can be cooked longer before they burn ... and burned garlic is bitter, acrid and will ruin any dish.  (if you burn garlic, stop immediately, trash everything, clean the pan, and start again -- there is no way to save it that I know)