When Lucas was talking about making three trilogies, he said that the droids (R2-D2 and C-3PO) were the only ones that would be in all three trilogies and in all nine movies (this was in the 70s, when he said there would be three trilogies).
He said the story was basically told through their eyes.
Excluding The Clone Wars (the movie and both animated series), here's the actors who were in both trilogies (but not always in all films): Anthony Daniels played C-3PO and Kenny Baker played R2-D2 in all six movies.
Frank Oz , as you have already mentioned, played Yoda's voice in five movies.
Ian McDiarmid played Senator/Chancellor/Emperor Palpatine (and Darth Sidious) in 4 movies (Episodes I-III and VI) originally, but was dubbed in for Episode V later .
So you could say he was in four of the movies when they were originally released, but is currently in 5 of the movies.
Also, as you pointed out, James Earl Jones was in four films as Vader's voice, and when Hayden Christensen was added in to Episode VI (replacing Sebastian Shaw at the end), he was in three films.
While some say Greedo showed up in 2 films , one in each trilogy, he was played by different actors in Episode I and Episode IV.
If the Special Editions are taken into account Temuera Morrison is in 3 films, playing Jango Fett and his clones in Episodes II and III and voicing Boba Fett in the Special Edition of Episode V.
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What about Chewbacca played by Peter Mayhew, he was in III and IV-VI
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You guys forgot Warwick Davis!
He played Wicket in Episode VI (in costume) and also had 4 (uncredited) appearances in Phantom Menace
He had four brief uncredited appearances in The Phantom Menace—one as W. Wald, the young Rodian friend of Anakin Skywalker; the other as Weazel, one of the gamblers at the podrace.
Davis also had a cameo as a "Tatooine street trader", and doubled Yoda in some of his "walking" scenes in Episode I
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The only characters to appear in both trilogies were Anakin Skywalker / Darth Vader, Obi-Wan Kenobi, The Emperor, R2-D2 and C-3PO, plus the muppet character Yoda.
The first two were played by other people, except the appearance of Hayden Christensen as you mention.
Ian McDiarmid played Emperor Palpatine (as Kev's answer mentions).
You also mentioned Yoda 's voice ( Frank Oz ).
On the subject of voices, James Earl Jones played Darth Vader 's voice in both trilogies.
Finally, Anthony Daniels played C-3PO and Kenny Baker played R2-D2 in both trilogies.
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Ian McDiarmid appears as the emperor in episodes
I, II, III and VI in the original trilogy.
He is also in the amended version of episode V, but not the original theatrical version.
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The only actor whose face can be seen in both trilogies is Ian McDiarmid (1, 2, 3, 6 added later to 5).
Another actor whose face can be seen is Hayden Christensen who was digitally added later into Ep. 6.
Others that appear on screen but with a body costume, are Peter Mayhew (3, 4, 5, 6), Anthony Daniels (all) and Kenny Baker (all).
And the actors that contributed with their voice are; James Earl Jones (3, 4, 5, 6) and Frank Oz (1, 2, 3, 5, 6).
Now that the cast for sequel trilogy is apparent, we might have some of these actors appear in 3 trilogies on top of obvious 4 appear in their 2nd.
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As I remember from seeing "The Empire strikes Back" preview before the initial Australian cinema release in 1980, the Emperor appeared at least in holographic communication with Darth Vader.
Vader moved his Star Destroyer to where he could get better reception first.
I don't know if that was Ian McDiarmid or another actor.
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Apart from the voice of Yoda,  Frank Oz , have there been any other actors who played a role in both trilogies? I suppose  Hayden Christensen  counts, having been recently included in the Blu Ray version of Episode VI.
Which Actors Were Featured in Both Star Wars Trilogies?
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Ian McDiarmid played Emperor Palpatine episodes 1,2, 3 5 and 6. Excluding  The Clone Wars, the following actors were in both trilogies (but not always in all films):  Peter Mayhew played Chewbacca, Anthony Daniels  played C-3PO and  Kenny Baker  played R2-D2 in all six movies, not forgetting Warwick Davis.  James Earl Jones and Frank Oz were both voice actors in both trilogies.  A number of actors make an appearance in both trilogies including Ian McDiarmid, Anthony Daniels, Kenny Baker, Peter Mayhew, Warwick Davis etc. 
Ian McDiarmid appeared in both trilogies. Anthony Daniels, Pete Mayhew and Kenny baker appeared in both trilogies. Warick Davis makes un-acredited appearances in both trilogies. James Earl Jones appears in both trilogies. Hayden Christensen appears in both trilogies.