The drop or offset of the shoe is something to consider. When you look at the foamy midsole, you'll generally notice more of the foam at the back of the shoe as compared to the front--so you are basically on a ramp of foam rising from toe to heel, and that's the drop or offset, usually noted in millimeters of height difference. A shoe that has no height difference (no more foam in back than front) would have zero offset--a zero drop shoe.
I don't know for certain that one type of offset is better than another. I favor a lower offset, feeling it might be easier for me to clear the heel (with less of it there) and land/strike more midfoot with my knee more flexed at impact. I think most agree that using shoes of different drops or offsets will work your tissues in different ways, stressing different muscles. It's recommended that you ease into mileage in a lower drop shoe if your tissues are used to being in a higher offset, as you will feel more in your calves and Achilles when working in the lower drop shoe.
Some have a collection of shoes of different drops and therefore work different tissues on different days. If you have shoes with different drops then you will probably find that you favor one type more than another.
It can be hard to tell by looking with the eye. The Brooks shoe below has an offset of 10mm while the Newton has an offset of 4.5mm. Ask us about different drops when you're in the shop--we know them all :)