They DO wear out. At the very tip of the blade, the outer tip of the cutting edge, it wears with use, and rounds over. When it's rounded, it'll affect cut quality. It happens because the effective cutting circle of the blade becomes smaller in diameter which reduces blade cutting path overlap, so if you have 3 blades, you'll begin to notice the mower cutting 3 paths instead of one wide path. Same thing happens as the blades are sharpened over and over, material is removed and makes the effective diameter of the blade's cutting path smaller.
The wings also wear down with use. Typically when mowing dusty areas or sandy areas, they'll wear a LOT faster. Same for mowing/mulching leaves and pine needles. They'll wear to the point where the wing gets thinner at the top/outside edge, and lots of times will wear where the bend starts. I've seen them develop a groove, sometimes crack because they get thin, sometimes the crack propogates and throws the remainder of the wing off somewhere (neighbor kid's face?). This is why it's important to keep an eye on them.
If you like a good cut quality, replace them as opposed to sharpening. Many will argue, but I have enough experience in lawn and garden (and my own landscaping company) to know that they do wear out and affect cut quality. Some customers like a fine golf-course style cut and those are the ones who will gripe if the stripes are 18" wide and uneven (on a 54" 3 blade deck). My yard is just exactly like that currently as my blades are worn. They don't look bad but they are worn and it's affecting cut quality. Time to replace them.
As far as sharpening, just use an angle grinder with the blade clamped in a vise. It doesn't make a huge difference on the angle and/or how even they are, if you look at brand new blades, they're not perfectly sharp-actually they have about a 1/32" flat edge at the face of the cutting edge which keeps them from getting dinged up and wearing so quickly. Balancing, I just use a screwdriver through the hole and put the tip of the screwdriver on the bench edge. The heaviest edge will fall obviously. I can tell no difference between doing it this way and precision balancing with a cone-style balancing jig; plus it's faster. I've also got an Oregon blade sharpener specifically made to sharpen mower blades and it does a good job, but takes forever and makes a TON of noise. I use it to touch up on newer blades that haven't been used much but really the angle grinder is faster, quieter, and does about the same thing.