Ah, deleted scenes -- the backbone of any good special features menu. When it comes to Star Wars, they can be hotly contested, due to The Almighty Canon. Some scenes offer additional insight into George Lucas's world, while others have been revisited or reworked in comics, books and TV shows. Then there's the vast majority of Star Wars deleted scenes, which either pad out or bog down already existing sequences -- in other words, they were probably deleted for a reason.
That said, the saga does include a few gems, which is why I pored over every Star Wars deleted scene and picked out what I think are the best ones from Episodes I-VII (listed in chronological order)...
Extended Podrace (The Phantom Menace)
The Scene: Introductions for all the racers and a longer lap two sequence. [Begins at 3:05]
Why It's Cool: Aside from maybe Duel of the Fates, the big podrace in Episode I is widely considered the best part of the movie. While many would argue it's long enough as it is and the CGI doesn't hold up as well as it used to, it was a crazy-ambitious set piece at the time, and Ben Burtt's sound design on it is still some his best work to date.
Okay, so the extended grid sequence is ridiculously long, a whopping seven minutes (most of which is comprised of turbine engine close-up porn), but the second lap includes some really fun moments like Sebulba blasting other racers with fire, one of Anakin's pods spinning out of control, and Jawas running out onto the field and scavenging for pod parts. (Regarding that last one, a similar visual was used in The Force Awakens when Jakku scavengers chased after a crashed TIE fighter during the Millennium Falcon chase.)
The Lost Twenty (Attack of the Clones)
The Scene: At the Jedi Temple Archive, Jocasta Nu explains to Obi-Wan Kenobi why Count Dooku left the Jedi Order. [Begins at 3:08]
Why It's Cool: This is a very brief scene, but it's notable for two reasons. First, on a pure storytelling level, it offers a clear and concise explanation of who Count Dooku is and how he ended up leaving the Jedi. (We glean this info much later, when Obi-Wan is captured). Second, this scene hints at the Lost Twenty, who were the only Jedi Masters in history to renounce the Order. While this is never explicitly stated in either the film or the deleted scene, the Lost Twenty were eventually made canon in 2015's Star Wars: Absolutely Everything You Need to Know.
Seeds of Rebellion (Revenge of the Sith)
The Scene: A small group of Republic senators discuss the possibility of forming of a rebel alliance in light of Chancellor Palpatine's recent dealings. [Begins at 7:28]
Why It's Cool: The Prequels often get a bad rap for being too talky and political, but Episode III's Rebel Alliance subplot was one of the few times politics seemed totally justified. Ironically, it was completely scrapped, but we still have three deleted scenes that explain how the likes of Bail Organa defected from the Empire and began their own splinter group, the future Rebellion. They also feature Genevieve O'Reilly as Mon Mothma, who will reprise her role in this year's Rogue One: A Star Wars Story.
Exiled to Dagobah (Revenge of the Sith)
The Scene: After parting ways with Obi-Wan and Bail Organa, Yoda arrives on the planet Dagobah, where he goes into hiding. [Begins at 14:16]
Why It's Cool: It's a little puzzling why this scene was left out of the movie when literally every other character got a scene showing where they ended up. While Yoda's fate is obvious to anyone who's seen Empire, so is pretty much everything else in the last 10 minutes of Sith. It would have been nice to see this last piece of the puzzle make it into the movie, but at least we still have this scene to show us exactly how Yoda arrived on the planet.
Tosche Station (A New Hope)
The Scene: After spotting two ships battling in space over Tatooine, Luke Skywalker rushes to Anchorhead and runs into his old friend Biggs Darklighter, back from the Imperial Academy. [Begins at 0:27]
Why It's Cool: Originally, this scene was Luke's introduction and gave us more context for why he wanted to join the Rebellion -- especially during his conversation with Biggs. Ultimately, we see Luke's inner conflict manifest in other, better ways, so it makes sense why this subplot was cut, but given that Biggs's other scene, on Yavin, was put back into the 1997 Special Edition, it's unclear why Lucas wouldn't have also wanted to include Tosche Station, which set up Biggs and Luke's relationship on Tatooine.
Wampa Attacks (The Empire Strikes Back)
The Scene: As it turns out, the rebels were harboring wampas in a closed-off section of Echo Base. When Darth Vader and his troops arrive, the creatures escape and begin wreaking havoc.
Why It's Cool: The idea of punching up Vader's arrival on Hoth is a good one. In Empire, he and his men are only seen in a handful of shots, and it's easy to forget they were even there. By adding a wampa outbreak, the Empire's assault on Echo Base might have been a little more dynamic and memorable.
Of course, the execution was hilariously bad, as evidenced by this deleted scene. At the time, ILM hadn't quite figured out the look of the wampas (creature designer Phil Tippett would go on to create the iconic version in the Special Editions), but it's still fun to see what might have been. There's also a great sight gag where C-3PO rips a warning sign off the wampa pen door, followed by a group of snowtroopers opening it and getting pulled inside by a wampa's arm.
Yoda's Test (The Empire Strikes Back)
The Scene: While training on Dagobah, Yoda instructs Luke to cut up a metal bar with his lightsaber. [Begins at 8:15]
Why It's Cool: Not a lot to this one, but it was always a little odd how Luke was never trained in lightsaber combat after his one lesson with Obi-Wan in Episode IV. It's interesting, then, to see that Yoda did at one point incorporate sword practice into Luke's training. Unfortunately, this scene's audio was never recorded, so we don't really know what the significance is of the metal bar or how it helped Luke hone his lightsaber skills.
Vader's Arrival and Reaching Out to Luke (Return of the Jedi)
The Scene: Vader reaches out to Luke through the Force. Meanwhile, on Tatooine, Luke has finished constructing his new lightsaber and sends R2-D2 and C-3PO to Jabba's Palace.
Why It's Cool: While seeing Luke put the finishing touches on his new Jedi weapon would have been a rad introduction for him, this scene's deletion is actually the best part about it. Not only does it bury the lead by focusing on the droids at the start (much like Episode IV), but it makes Luke's actual introduction that much more dramatic when he arrives at Jabba's Palace. Plus, it conceals the fact that Luke had hidden his lightsaber inside Artoo, which, again, makes that reveal so much more rewarding. In this case, less is definitely more.
The Lost Rebels (Return of the Jedi)
The Scene: A compilation of rebel pilots who never made it into the Battle of Endor, along with footage of General Madine replacing Admiral Ackbar, in the event that the puppet didn't look convincing. [Begins at 0:08]
Why It's Cool: Not so much a "deleted scene" as "deleted coverage," this footage shows an unedited look at some of the screen tests that were done for the Battle of Endor. The first half is comprised of various actors being fed lines that are then repeated in rapid succession. As it happens, the performers include two female humans, a Sullustan and another Mon Calamari. The second half shows Madine in Ackbar's moving chair and reciting his lines. (Alas, no Madine version of "It's a trap!")
Tunnel Standoff (The Force Awakens)
The Scene: As the First Order begins its assault on Takodana, Han Solo, Finn and Chewbacca try to escape Maz's castle but are halted by a team of stormtroopers.
Why It's Cool: This scene is basically just Han talking his way out of a gunfight, but it's also Harrison Ford at his finest. In addition to making several hilarious quips ("What makes him supreme?"), he makes an offhand remark about Finn's stormtrooper boots -- which explains how his character knew Finn was lying about being with the Resistance. Presumably, this sequence would have led to Maz Kanata using her silly not-Force powers to collapse the ceiling, so maybe it was a blessing in disguise that this sequence didn't make the cut. Otherwise, though, it's pure character.