Clearing the Shire of Orcs and Goblins

The movies as a whole primarily tell the story of the destruction of the ring. So when the ring is destroyed, that is the climax of the movie, and movies almost always end shortly after the climax.

I read the books for the first time shortly after the first movie came out, and when the ring was destroyed only halfway though book 6 (the second half of Return of the King), I remember being confused, thinking "ok, so what's the rest of the book about?" After I read it, I thought to myself "no way is this going to make it into the movies".

It's not that it isn't important to the world that was built by the books, but Tolkien's writings go into a lot of detail to create an entire history behind his world. The movies, on the other hand, are following a more typical film structure, telling a single (though complex) story about trying to stop the return of Sauron by destroying the ring. To introduce the scouring of the Shire after the ring is destroyed would have required a lot more time, and would have gone against the typical way in which films tell stories.

The books of The Lord of the Rings have several side-adventures and subplots which greatly flesh out Middle Earth and the characters of the story, but would add quite a bit of time to an already epic-length movie trilogy (yes, Jackson added his own subplots to the movies which ate up more time, but my point still stands).

For example, Tom Bombadil added very little to the story as a whole, serving primarily (in the grand scheme of things) to provide the hobbits with their blades. Aragorn did the same thing in about five seconds on screen.

The Scouring of the Shire tied up some loose ends: where did Saruman go after he left Isengard? Gandalf mentioned that Sauron would eventually turn his attention to the Shire, if nothing else because while hobbits are of very little concern to him, he would take pleasure in their slavery and strife. Furthermore, Frodo saw death and destruction in Galadrial's Mirror. What happens to the Shire? After over a year of adventuring across lands the hobbits only heard of in stories, how have they matured and grown strong? This part of the story ties up all of these questions very decisively.

However, the story as told by the movie is focused on the destruction of the ring. The Scouring of the Shire could certainly have been included and would have been an interesting second climax: just when you thought the story was over and the heroes could go home, the heroes find their home under attack by villain #2. However, the movies were already very, very long, and several parts of the story had to be cut to make the movies a reasonable length to sit through in the theater and to provide more screen time for Liv Tyler. By killing Saruman at Orthanc in the movie, his story arc in the Shire never transpired and that whole subplot could be cut.

TLDR: time. While the subplot did tie up loose ends and demonstrates how the hobbits grew from "little people" into brave warriors, it was not absolutely essential to the story of destroying the ring and its omission made it easier to sit through a movie that was already difficult enough to sit through without a bathroom break (in the theater).

In the movie, Peter Jackson made the choice to paint Merry and Pippin as more fool-hardy than they actually are in the book.

For example, one of the two (can't remember which at the moment) were actually in charge of getting Frodo set up in a different town from Bag End, with the intention of deceiving anyone that might come looking for Frodo. This was a very important task given by Frodo, showing how much he trusted the two.

It was later that the two announced to Frodo that they know what he's up to, and tell him they refuse to leave him on his own.

Both Merry and Pippin, in the book, show a lot more courage and trust than in the movies.

The movies painted these two and more careless. I think this was done to show that they are mentally younger than Frodo, albeit they looked roughly the same age. I think it was also done to add some comic relief to the movie.

So, in essence, the movie stripped away this important part of Merry and Pippin because it didn't really fit in with the way the movie portrayed the two.

The Return of the King was already well over three hours long. The ending already felt bloated after Sauron was defeated, jumping from the Fellowship's reunion to Aragorn's coronation to the Shire to the Gray Havens. An argument could be made that this should have been two movies, but it was not, and it was not feasible to squeeze in the redemption of the Shire.

Correction: The Shire is overrun by human ruffians, not Orcs.

"The Scouring of the Shire" is the penultimate chapter of the epic fantasy The Lord of the Rings by J. R. R. Tolkien and the eighteenth chapter of The Return of the King. The hobbits, Frodo, Sam, Merry, and Pippin, return home to the Shire to find that it has been despoiled and corrupted by ruffians and their leader, the wizard Saruman, now known as Sharkey. To date, it has been left out of all film adaptations of the novel.

Source: Wikipedia. Emphasis is mine

Why the scene was left out has been addressed here and on sci-fi.se:

After 9 hours setting up two huge battles to conclude the movie in an epic fashion, the expulsion of a few ruffians from The Shire is just... well... dull. Boring. And most importantly, not fit for a movie, not cinematic enough, just like the whole Tom Bombadil part.

Source: Quoting from sci-fi.se. Hat tip to @Janoma