The Clone Wars - S3E8 - "Evil Plans"

9:04 - C-3PO (to Cad Bane):  "I don't know what you're talking about."  Perhaps coincidentally, Leia also says this (to Vader) in A New Hope [7:56].

9:10 - C-3PO:  "I am a protocol droid, human-cyborg relations."  He uses the same phrase when he introduces himself to Padmé and to R2-D2 in The Phantom Menace ("I am C-3PO, human-cyborg relations" [39:03 and 39:26]), to Luke in A New Hope ("And I am C-3PO, human-cyborg relations" [20:25]), and to Lando in The Empire Strikes Back ("I am C-3PO, human-cyborg relations" [1:21:31]).  He's about to say the same thing in Return of the Jedi, but EV-9D9 interrupts him, so he gets only as far as "I am C-3PO human-cy-" [11:21].

9:41 - C-3PO:  "I am fluent in over six million forms of communication."  He says almost the same thing in The Empire Strikes Back ("I am fluent in six million forms of communication" [18:38]) and twice in Return of the Jedi ("I am fluent in over six million forms of communication and can readily-" when he's interrupted by EV-9D9 [11:29] and "I am fluent in over six million forms of co-" when he's interrupted by Han Solo [1:11:10]).

14:17 - Cad Bane (to R2-D2, referring to C-3PO):  "Your friend Goldenrod turned out to be a huge waste of my time."  In The Empire Strikes Back, Han Solo also uses this moniker:  "Hurry up, Goldenrod; you're gonna be a permanent resident!" [34:30].

15:24 - Padmé:  "Where can 3PO be?"  Luke has a similar line in A New Hope as he's trying to raise C-3PO on his comlink:  "Where could he be?" [1:22:12 and 1:23:19, the second followed by "3PO!"].  C-3PO himself has a similar line a bit later in A New Hope:  "Where could they be?" [1:29:33].

16:13 - C-3PO:  "We'll be deactivated for sure."  He has two similar lines near the beginning of A New Hope:  "We'll be destroyed for sure!" (referring to himself and R2-D2) [2:50] and "You'll be deactivated for sure!" (referring just to R2) [6:39].

The Clone Wars - S3E7 - "Assassin"

5:47 - Yoda:  "Always in motion is the future."  He also says this in The Empire Strikes Back [1:17:54].

14:56:  One of the citizens of Alderaan (far left) in the applauding crowd has clothing and a hair style that are apparently meant to be reminiscent of Leia's in A New Hope.

16:55 - Padmé:  "And if you strike my voice down, know that a chorus of thousands shall rise up in its place."  The first part of this resembles what Obi-Wan says to Vader in A New Hope:  "If you strike me down, I shall become more powerful than you can possibly imagine" [1:30:48].

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At 2:37, there's a very brief musical cue of Yoda's theme, and at 8:35, Leia's theme is heard, which Dave Filoni mentions in the episode featurette on the Star Wars website.

The Clone Wars - S3E6 - "The Academy"

5:32 - Cadet Lagos:  "I have a bad feeling about this."

17:01 - Satine:  "Ashoka, it's a trap."  Admiral Ackbar says, "It's a trap!" in Return of the Jedi [1:35:03], and Leia says it twice in The Empire Strikes Back [1:39:50].

17:25 - Almec:  "Set for stun."  In A New Hope, one of the stormtroopers aboard the Tantive IV also says this [6:24], and in The Empire Strikes Back, it's part of Vader's instructions to Admiral Piett:  "Prepare the boarding party, and set your weapons for stun" [1:57:09].

The Clone Wars - S3E5 - "Corruption"

[I don't have anything to say about this episode yet, but I didn't want to skip over it.  This post is acting as a place holder, and I'll update it in the future if I find something to note.]

The Clone Wars - S3E4 - "Sphere of Influence"

13:21 - Greedo's dice have the same design as Watto's in The Phantom Menace [53:40]:

17:18 - Senator Chuchi:  "Where's your sister?"

Che Amanwe:  "I don't know; we were separated."

There's a similar exchange in Return of the Jedi where Han asks Luke, "Where's Leia?" and Luke explains that "We got separated" [1:02:15].