Why are there so many different pasta shapes?

One answer to this is that Americans have a reversed understanding of the relationship of pasta to sauce compared to Italians. In Italy, the sauce is called the condimento, meaning literally it is a condiment to the noodles, which are intended to be the main source of enjoyment in the dish. When you begin to understand it that way, it makes sense that you would want to have a wide variety of sizes, shapes and textures. (What Taeraresh said is also true, there are functional differences in how the different shapes hold sauces.)

One thing that varies is how much of the sauce adheres to the pasta, especially for pasta shapes that have ridges or hollow areas. Sometimes you'll have a sauce where you'll want chunks of it to stick to the pasta, and sometimes you just want the pasta to be flavored by the sauce, but eaten more by itself.

It's regional varieties -- just as there's different cheeses and olives, different types of pastas have evolved.

Now, you might think at first that it doesn't make sense, as we could produce the same pasta everywhere, you have to remember that Italians will pair specific sauces with specific pasta to get a specific balance of sauce to pasta. As different things are grown / raised / etc in different areas, we end up with different pastas preferred for different sauces. Some are better for oil (eg, thin strands, light and delicate), some for cream sauces (wider strands, tubes), some for tomato sauces (wider strands, anything with good ridges on it), some for soups (smaller shapes), etc.

Now, I know, there's lots of tubes, and there's lots of strands ... but others could ask why Americans need Coke, Pepsi and RC Cola (although, in that case, there's commercial interest, but there's still some heavy regional preferences out there, particularly for smaller local varieties)

As for the difference between penne vs. ziti -- the angle of the cut on the end can affect how much sauce gets inside the pasta, as the angled cut of the penne will grab some as you're stirring the pasta in the sauce. (or so I've been told ... I've never done a side-by-side comparison of two with the same diameter / thickness / length, etc.)

Mainly that different shapes serve different purposes. You should pair the right kind of pasta with the right kind of sauce. Depending on sauce thickness or what's in it etc.

Some shapes are also designed to allow for different textures like farfale where the core cooks less than the edges, making for a richer texture.

Whilst there may be pasta shapes designed to be decorative rather than functional most pasta shapes serve a clear purpose. Spaghetti, for example holds a pesto or a finely ground beef sauce very well, whereas if you used a thicker pasta noodle for something like pesto or just a simple olive oil and garlic dressing there would be too much pasta per forkful to flavouring. Yet a thick tagliatelle would be very suited to a game pasta sauce made with chunks of rabbit or hare. Chunky vegetable sauces work very well with large pasta shells, as the shells catch the vegetable pieces in the sauce, making it easier to eat. Tubular pasta works very well with creamy sauces (such as macaroni and cheese) because it is very satisfying to bite into the tube and feel the sauce releases within. You could also say that so many shapes exist to satisfy the individual's personal taste and sense of fun.

The pasta cooks differently based on the shape. It will have a different feel in the mouth, and as you chew, as well as holding the sauce differently.

You will notice the difference most if you aim to cook the pasta perfectly al dente.

We were sitting at a table in the town square of Sienna, Italy having drinks. My wife and mother-in-law went off to do some shopping. I wandered off down a narrow street and came to a pasta shop. The interesting thing that might answer some of the question is found there, I think. The wall was covered with cubby holes similar to an old time post office ending in glass front drawers about waist high. Arranged vertically were compartments holding the largest diameter spaghetti (or macaroni as they say) down to Angel hair at the bottom. There were a variety of shapes all in descending diameters. The drawers held shapes, such as, stars, elbows, rotini, etc., in different sizes and thicknesses. It occurred to me that the people eat pasta so often, they use the different shapes and sizes to break the monotony of just spaghetti, let's say. Also, they could have a different sauce to go with each pasta shape or size. Makes sense to me now and then.