What is the "standout" piece for each episode?

For me...

ANH: The Battle of Yavin, Tie Fighter Attack and The Throne Room. Can't pick one.
ESB: Imperial March and The Rebel Fleet/End Titles are incredible.
ROTJ: Parade of the Ewoks and The Battle of Endor II and III.
TPM: Duel of the Fates, no competition.
AOTC: Across the Stars, and that's the only real standout. The weakest of the seven IMO.
ROTS: Battle of the Heroes, Padme's Ruminations and Anakin's Betrayal are the biggies.
TFA: Rey's Theme and The Jedi Steps - both outstanding.

 

The Phantom Menace: Gah, I have to go with Duel of the Fates. It ranks as my #4 favorite out of ALL of the songs in Star Wars.
Attack of the Clones: I love Across the Stars, but something about The Arena just makes me want to choose it
Revenge of the Sith: Since I really dig choirs, I would choose Battle of the Heroes, but obviously I must go with Anakin vs Obi-Wan
A New Hope: Binary Sunset, hands down. John Williams makes the musi that is so great, you cry. Well, um, at last I do......
The Empire Strikes Back: Imperial March!!!!! Although I have a soft spot for Yoda's Theme: Mysterious, yet hopeful.
Return of the Jedi: Pit of Carkoon, Han Solo Returns....so many good pieces. Except Jedi Rocks, lol. Ok, I'll go with Victory Celebration. It uses pipes and drums more than the typical strings, which I liked.
The Force Awakens: Williams made Main Title so much more magical this time. Rey's Theme was good, too. But I simply must go with The Jedi Steps/Finale. That's when everyone screams, "HE'S BACK!" It is a great piece, though.

 

TPM: Duel of the Fates. The best piece in the film by along shot, full of energy and suspense.
AOTC: Can't really remember anything that makes me go wow, although The Arena sequence is decent.
ROTS: General Grievous or Grievous talks to Sidious: two similar pieces that convey a far better character than was actually presented. Sinister yet still energetic.
SW: Very hard to choose. The main theme is legendary of course, Binary Sunset is very well constructed with a brilliant use of dynamics to produce a very dramatic emphasis, The Final Battle traces wonderfully the events and is full of emotion, and Throne Room is very uplifting and powerful. I'll go for the Main Theme just because it is so iconic and powerful.
TESB: Imperial March. Needs no explanation. Most iconic villain theme of all time?
ROTJ: Emperor's Throne Room, maybe? Not sure here.
TFA: Jedi Steps/Finale, without doubt. Most powerful moment of the film is conveyed entirely through the music and camerawork. No dialogue needed.

 

TPM: Duel of the Fates
AOTC: Across the Stars
ROTS: Battle of the Heroes
ANH: Binary Sunset
ESB: Imperial March
ROTJ: Victory Celebration
TFA: Rey’s Theme

 

This is exactly my list, though The Jedi Steps gives Rey's Theme fierce competition. I think this ranking is also most likely the averaged ranking as far as what people would consider the most iconic piece from each film, with only ANH (Main Theme) and ROTJ (several, especially the Emperor's Theme) having competition. I just love how naturalistic and unique Victory Celebration sounds in comparison to the rest of saga. The brass dominates the saga and Williams is a master of it, so the way the woodwinds take center stage here truly felt like a rebirth for the galaxy.

 

TPM: Duel of the Fates
AotC: Across The Stars
RotS: Anakin's Dark Deeds
ANH: Binary Sunset
ESB: Yoda's theme
RotJ: Parade of the Ewoks
TFA: The Jedi Steps and Finale

 

TPM: Duel of the Fates 2nd: Trade Federation March
AOTC: Across the Stars
ROTS: Anakin vs Obi-wan 2nd: Jedi Temple March
ANH: Binary Sunset 2nd TIE Fighter Attack
TESB: Imperial March 2nd: The Rebel Fleet
ROTJ: Emperor's Theme 2nd: The Battle Of Endor II when Lando finds out that thing's operational, or Endor III with the chorus and Luke, Vader, Emperor themes
TFA: Rey's Theme very close 2nd and my favorite: The Jedi Steps. Farewell and The Trip with Rey's theme leading into The Jedi Steps is beautiful

 

Obi-Wan Catnobi Binary Sunset, Burning Homestead, Learn About the Force... I cry too

 

TPM: Duel of the Fates
AOTC: Across the Stars
ROTS: Padme's Ruminations
ANH: Binary Sunset
TESB: The Imperial March
ROTJ: Emperor's Throne Room
TFA: Nothing stood out for me here, so can't choose.

 

Going by the track titles of the versions I have:

TPM: Duel of the Fates
AOTC: Across the Stars
ROTS: Battle of the Heroes
ANH: Main Title/Rebel Blockade Runner
TESB: The Imperial March (Darth Vader's Theme)
ROTJ: The Battle of Endor II (specifically, the throne room duel climax)
TFA: Rey's Theme

Honorable Mentions
TPM: The Droid Invasion and The Appearance of Darth Maul, The Arrival at Tatooine and The Flag Parade
AOTC: Zam the Assassin and the Chase Through Coruscant
ROTS: Anakin's Dark Deeds, Star Wars and the Revenge of the Sith
ANH: The Hologram/Binary Sunset, Cantina Band, Ben Kenobi's Death/TIE Fighter Attack, The The Battle of Yavin, Throne Room/End Title
ESB: The Battle of Hoth, The Asteroid Field, Yoda's Theme, The Clash of Lightsabers/The Stormtroopers Are Coming
ROTJ: The Pit of Carkoon/Sail Barge Assault, Parade of the Ewoks
TFA: The Jedi Steps and Finale, March of the Resistance

 

I made a point of not reading the other posts, since I wanted to make my list as uninflueced as possible.

I'm not going to count the main Star Wars them, since it's central to all the movies. Love it, though

TMP: "The Droid Invasion" or whatever that main theme for the droid army is called (they play it when the army first lands on Naboo and later enters the capital)
AOTC: "Across the Stars" (to be honest, this is movie has my least favorite Star Wars soundtrack and I don't really have a favorite piece from it)
ROTS: "The Immolation Scene" (the Order 66 montage)

ANH: "Binary Sunset"
ESB: Imperial March (that's almost a cheat; "Yoda's Theme" is a close second, but Imperial March is my favorite Star Wars music)
ROTJ: "Victory Celebration" (I like that Ewok theme, too)

TFA: "Rey's Theme" (I suppose I should throw "The Scavenger" in there as well; it's basically the same thing. I've never really understood the idea that Force Awakens had weak music. Oh, well.)

And as a bonus, the Clone Wars movie: "Star Wars Main Title & A Galaxy Divided"

Okay, now time to see everyone else's lists.

 

Immolation Scene is when Anakin is being burnt
Music that plays during Order 66 is Anakin's Betrayal

 

TPM: Duel of the Fates
AOTC: Across the Stars
ROTS: I honestly can't remember anything that sticks out as memorable to me
ANH: The Force Theme, The end sequence
ESB: Everything from the movie
ROTJ: The track that plays as the Rebels begin their attack on the Death Star, Luke and Vader's final duel
TFA: Rey's Theme, March of the Resistance

 

TPM: Duel of the Fates
AOTC: Across the Stars
ROTS: Battle of the Heroes
ANH: Binary Sunset
TESB: Imperial March
ROTJ: Into the Trap
TFA: Rey's theme

 

I started out wanting to write standout pieces for each film, but I just couldn't. It's all too good. Seriously, the soundtracks of these films are good across the board. So, instead of writing a standpoint piece of each (perhaps impossible, beyond what others here have listed), I will write what I believe are completely overlooked tracks that are actually incredible. They aren't necessarily my favorite from each film, but I think they deserve more attention because they are fantastic.

- The Phantom Menace: Swimming to Otoh Gunga, The Racer Roars to Life, and Anakin is Free
- Attack of the Clones: Making Contact, Return to Tatooine, and Shmi's Funeral
- Revenge of the Sith: Anakin's Dream, Rise of the Empire (It Can't Be), and Padme's Funeral*
- Star Wars: Tales of a Jedi Knight, Burning Homestead, and Destruction of Alderaan
- Empire Strikes Back: Training of a Jedi Knight, Lando's Palace/Beware the Dark Side, and Rescue from Cloud City
- Return of the Jedi: Approaching the Death Star, Brother and Sister, and Leia's News/Funeral Pyre for a Jedi
- The Force Awakens: Attack on Jakku Village, The Scavenger, and Finn's Confession

*- I would be remiss if I didn't mention how amazing the overlooked track 'Padme's Visit' is as well. Perhaps the most tragic rendition of 'Across the Stars' is heard here.
You can also hear a rather tragic but beautiful rendition of it at the end of the 'End Credits' of Attack of the Clones.

 

TPM: "Duel of the Fates"
AOTC: "Across the Stars"
ROTS: "Battle of the Heroes"
ANH: "Princess Leia's Theme," "Binary Sunset, " "Ben's Death and Tie Fighter Attack."
TESB: "The Imperial March"
ROTJ: "The Emperor's Theme"
TFA: "Rey's Theme" and "The Jedi Steps."