Why and what kind of breads should be scored?

A properly formed loaf, before it is baked, has a network of gluten strands stretched tightly around its perimeter. This network is in tension, helping maintain the shape of the loaf.

There are several reasons to score the loaf:

• The tension in the outer network of gluten strands limits the ability of the loaf to expand, especially in the "oven spring" or final excited burst of activity that the yeast go through as the temperature of the dough rises at the beginning of baking. The score creates a slit in the network, allowing the loaf to expand, permitting more oven spring to take place.

• The scores provide a weak point (due to the cut in that gluten net), controlling where expansion takes place oven spring proceeds. This may prevent cracks that would otherwise be unattractive.

• Furthermore, the score allows aesthetically pleasing shapes or patterns to created on the loaf, as the the dough exposed during oven spring will have a slightly different texture (it isn't surrounded by the in-tension gluten network, and will have been baked slightly less as it comes to the surface of the loaf during the oven spring). This means it will tend to have a different (often lighter) color than the main crust where the in-tension network was in place. For example:

  

  (credit on photo)

  Another example, taken farther for a more artistic statement:

  

  You can see the attractive pattern on the loaf from the scores (which are also functional in the first sense)—the look like a leaf. (Credit on photo).

Scoring is more important and effective in free form loaves which will have good oven spring.

SAJ14SAJ's answer is great. I will add one observation to answer the question: "What will happen if we don't score the breads?" In most cases, you just don't get as much expansion in the loaf. But if you shaped your loaves tightly and have strong yeast, something like this can happen. Basically, the yeast growth and air expansion inside your loaf can literally blow a giant hole (or two) in your crust. Normally when this happens, you just get some ugly cracking in the crust, but sometimes it's more dramatic as in the linked photos.

One other quick note: don't necessarily follow the advice on the linked page that says "always slash a half-inch deep with a serrated bread knife." While a sharp serrated knife can be used, a razor blade or very sharp straight blade knife will produce a cleaner cut without jagged edges. (If you don't have a sharp straight knife, though, you'll probably have better luck with a serrated knife.) Also, a half-inch deep cut is probably the maximum that will be effective, and often you only need to make a shallow slit through the tight skin layer (maybe 1/4" or even less). Making deeper cuts will sometimes deflate your loaves and/or cause them to spread sideways (rather than rising up). The best guidance is not to put any pressure into the cut, and let the blade do the work. Think of it like slitting an envelope: fast with a light touch is all that is necessary -- if the interior of the loaf has the strength to expand in the oven, it will pull that small slit further apart.

If you score the loaves with the blade at an angle (nearly parallel with the surface of the bread), that can help to produce "ears" on the loaf, where the sides of the slashed crust actually rise up away from the surface slightly. Aside from producing a visual effect that some artisan bakers find attractive, the "ears" also tend to help oven spring slightly more than a vertical cut.

When you subject the dough to the heat of the oven the air in it starts to expand, causing the bread to rise. If your dough is not scored then it will crack in the most unexpected places (because the air is trying to get out). Also, scoring ensures that you won't get large pockets of air in your bread.

Scoring is quite optional IMHO

So many opinions. My experience, even after doing an excellent bread-making course, is.. as long as you understand the principles then whatever works for you is fine... and make sure you have fun! I have scored over-proofed loaves that simply collapse as a result and have decided that if I let it proof a little too long it's better not to score as it won't rise much more anyway. And a sharp, straight blade definitely works better for me... but others have different experiences. I'm mainly a sour-dough man and I love those big air holes that show me that the flavour has developed nicely too.