In what order should a newcomer watch Star Wars episodes?

The Machete Order seems to be a great idea. It is a variation of the method @Nobby suggested, but it leaves out Episode I completely.

So the order is: IV, V, II, III, VI

The article is long but worth reading, it makes a lot of great points.

A little extract on why Episode I is unnecessary:

Episode I is a failure on every possible level. (...) Luckily, George Lucas has done everyone a favor by making the content of Episode I completely irrelevant to the rest of the series. Seriously, think about it for a minute. Name as many things as you can that happen in Episode I and actually help flesh out the story in any subsequent episode. (...) Every character established in Episode I is either killed or removed before it ends (Darth Maul, Qui-Gon, Chancellor Valorum), unimportant (Nute Gunray, Watto), or established better in a later episode (Mace Windu, Darth Sidious).

(already added it as a comment, but I think it deserves its own answer)

I am watching the films with my little boy, and am using a new method that seems to be the most agreeable:

• Ep. 4 - A New Hope

• Ep. 5 - The Empire Strikes Back,

• then go back and watch the three prequels as a sort of 'flashback'

• Ep. 6 - Return of the Jedi.

In this way, your child gets the full story of Anakin's rise, fall and redemption, without the big 'Father' surprise being spoiled.

I recently rewatched it in the order IV, (I, II), V, (III), VI (prequels bracketed for clarity), which I first saw proposed in this related answer. Now I can't personally speak about the impressions of a "newcomer" or if it's the "best" order possible, but it certainly has its advantages and is at least worth mentioning.

• It includes all the live-action films of the official Star Wars movie series, which has always been at the core of the whole Star Wars franchise. While many people don't like the prequels that much compared to the original trilogy, we're not here to debate about the individual movies' quality, but to watch Star Wars! And while the reasoning about I's story-wise irrelevance that is behind "Machete Order" is not that untrue, I for myself would not regard an order that leaves out a film from the official live-action movie series a complete viewing.

• It provides a nice varying mixture of originals and prequels. Decide for yourself if that is a good thing or not. But this is an order that provides the most variety between old and new (from the few reasonable orders at least). While it is similar in its intent of giving a kind of flashback, as the order provided in Nobby's answer (or the "Machete Order" derived from that), it drives this even further and spreads the flashbacks a bit more. And this way it might even be better at highlighting the "mirroring games that George Lucas was playing in the prequels" as described in Richard's answer.

• From a "spoiler" viewpoint of discovering the story unbenknownst to its outcome, it might actually be the best order. Neither is the original trilogy "spoiled" by the prequels, nor do the originals make revelations about the prequels, at least as far as possible. While I can't support that view myself, there are people who generally consider prequels less worth simply because of the fact that you already know how characters end up. This order tries to avoid that feeling as much as possible, even if it might not have been what Mr. Lucas intended.

  Now first of all, it doesn't destroy the big reveal in V about

  Vader being Luke's father. If you really think about it, while II does already show Anakin as a little bit troubled, it is not until III that we see his ultimate moral demise (and if you wouldn't know, you'd never assume that family connection anyway).

  But in the same way that we don't know this truth before V, while watching I and II we also don't know that Anakin, one of the main heroes,

  ends up as the ultimate bad guy either. All we do is wait for that Vader guy to betray and kill our beloved Anakin.

  And even more than that, the emperor isn't "spoiled" either. It is not until the very last scene of II (if at all) that we start to realize

  that Palpatine might actually be behind all those evil schemes.

  And in the same way, it is not until the following V that you even learn about this cloaked emperor guy still existing in the originals, too.

The Vulture website has aggregated the suggested viewing orders from a range of people involved in the original, prequel and new trilogies

George Lucas (I, II, III, IV, V, VI): “Start with one. That’s the way to do it right: 1, 2, 3, 4, 5, 6. That’s the way they’re supposed to be done. Just because it took a long time to film it doesn’t mean you don’t do it in order.”

Daisy Ridley (I, II, III, IV, V, VI): "I would say 1, 2, 3, 4, 5, 6, because for a young person it's easier to understand the chronology."

John Boyega (?): "I would say whatever you want! Watch 3, 6, 2, 1 — do whatever you want to do so long as you experience it a very unique way and enjoy it."

Mark Ruffalo (IV, V, VI, I, II, III): "From the first one made to the most recent. Straight through. They just build up nicely that way. That’s the way I saw it, and I’m a little bit of a throwback."

Aaron Paul (IV, V, VI, I, II, III): "You start with the original Star Wars movie. There is no other way. Maybe it’s nostalgia. Or maybe it’s not even that. I have no idea why I feel this way, but you should watch them in the order they were released."

They also offered the advice of a professional movie critic

Matt Zoller Seitz, critic (IV, V, I, II, III, VI): "The Godfather, Part II order. This is the order my wife came up with back in 2005. We were discussing the right order in which to show the movies to our kids, and we agreed that Darth Vader's reveal was such a big deal that it would be a shame to ruin it by showing the episodes in numerical order. She was a big fan of The Godfather, Part II, which flashes back and forth between Michael Corleone in 1959 and his father Vito as a young man in the late 19th and early 20th centuries."

"In this order, you start with A New Hope and continue through Empire, which of course ends with Vader dropping that huge plot bomb on Luke. Then you "flash back" to The Phantom Menace, Attack of the Clones, and then Revenge of the Sith to show how Anakin became Darth Vader. Then you finish with Return of the Jedi, where Luke tries to pull his father back from the Dark Side and at least partially redeem him, restoring balance to the Force in the process. We actually watched the films this way, and it really worked.

"Not only did it magnify the impact of the throne-room scenes in Jedi, it made it much easier to see the mirroring games that George Lucas was playing in the prequels, making The Phantom Menace a rhyme of A New Hope, The Empire Strikes Back with Attack of the Clones (right down to the sad cliff-hanger ending), and Jedi the answer to Sith, following right on its armored heels."

In chronological order, they are:

The Prequels

Star Wars Episode I: The Phantom Menace

Star Wars Episode II: Attack of the Clones

Star Wars Episode III: Revenge of the Sith

The Original Trilogy

Star Wars Episode IV: A New Hope

Star Wars Episode V: The Empire Strikes Back

Star Wars Episode VI: Return of the Jedi

As for optimum, no one can tell you that since we don't know what the new movie will be about.

I would suggest watching them in the order they were made IV, V, VI, I, II, III and then make your own mind up whether to watch The Clone Wars film or not (I think it depends on how much you enjoyed the prequel trilogy).

I usually skip I and II, though when I watch them through occasionally I may watch parts of Episode I such as the Darth Maul fight but I can't stand Episode II for me despite it setting up the Clone Wars crisis and the origin of the Clones, I find the whole Anakin plot line tedious in that film but it really depends on what you feel is best. If you're watching it with your kids you might want to start with the prequels as they are more on a children's level, well the first two anyway particularly having Jar Jar in the first one prominently.

But if it's just you wanting to watch them I definitely recommend watching them in order of creation, the whole setup in Episode IV is brilliant when you haven't got the prequel explanations as the characters (Obi Wan Kenobi and Darth Vader) have much more mystery surrounding them and the whole feud between Jedi and Sith plays out much better in my opinion through the original trilogy.