Don’t remember title or author* but I do remember a plot where an enhanced Chimp is on trial to determine if he’s entitled to the protections of a “person.” Written in the 60’s and the civil rights theme is overpowering.
*Glad to be able to be of so much help. 
I’m sure someone will be along shortly to remind me.
LAWYER: Stern, the prosecution’s got ya dead to rights! Yer guilty as a cat in a goldfish bowl! The best we can hope for is to get ya buried in secret so yer grave don’t get violated!
CAPTAIN STERN: I told you, Charlie, I got an angle!
Always loved that exchange. 
“Jerry Was a Man” by Heinlein.
Fantasy genre, but Piers Anthony has several trial scenes in the Xanth series that, similar to the OP’s example of the judge being able to read emotion, utilises the special circumstances of a magical world to add an interesting element to the proceedings.
See post #5!
Eric Flint and Dave Freer’s The Rats, the Vats, and the Ugly has three courts martial which provide a lot of the focus for the action of the story.
Isaac Asimov’s I, Robot I think had a trial scene in one of the stories, too.
Mike Resnick’s Second Contact begins with an officer being charged with murder, and the book focuses on the defense counsel’s struggle to prove the officer’s version of events. I can’t recall whether there’s actual trial scenery, but the fact of the trial is central to the book.
Taylor’s trial for heresy in Planet of the Apes
Right title, wriong story and author. And I’m surprised no one else mentioned it.
Eando Binder’s original short story I, Robot featured a robot on trial for killing its creator. A biog part of the issue was whether a robot even had a right to a trial.
The storty was made into an episode of the original Outer Limits, then redone for the reincarnated Outer Limits.
Despite the TV endings, Adam Link (the Robot) went on to other things. The short stories were collected as the book Adam Link – Robot.
(“Eando Binder” was the pen name of the Binder Brothers, Earl and Otto – hence “E and O” Binder.)
I found a few books by David Gerrold, a series starting with Jumping off the Planet, which have trials in them. Has anyone read these books? Are they worth searching for? How are the trials written, are they realistic?
Lloyd Biggle Jr.'s Monument has some trial scenes in it when the natives of a planet are attempting to save it from being despoiled.
In the Star Trek:TNG episode “The Drumhead”, A crewperson was found to be part Romulan, but not guilty of whatever crime it was.
http://www.startrek.com/startrek/view/library/episodes/TNG/detail/68496.html
It had a great Picard quote about evil not always the twirling-mustache kind, but that the more evil evil is cloaked in good.
Brian
No. The question was not, is Data a legal entity that we refer to ficticiously as a “person”?, but instead was, is Data a human being that’s made out of something other than flesh? Corporate and other juridical persons are not actually people.
–Cliffy
Say, don’t forget Asimov’s story (and the later novel and even later movie) Bicentennial Man, in which Andrew repeatedly goes to court to have himself declatred “human”.
(Unless someone already posted this and I missed it)
And I, for one, think Bicentennial Man was a fairly decent flick. God knows it “felt” more like an Asimov film than I, Robot.
The big problem I had with Bicentennial Man was that US (and presumably world) society was all Anglo-Saxon for the next 200 years.
Following up on Sage Rat’s mention of Xanth, one trial that definitely occurred in Xanth was that of skeleton Grace’l Ossein (for not acting scary in a bad dream for a troll) in Heaven Cent.
And in his Apprentice Adept series (last book, Juxtaposition…no, do NOT tell me there were books after that) Stile was place on trial on Photon for wanting to marry the robot Sheen, or something like that…don’t recall the precise charges.
IIRC, it was Kirk and McCoy who were tried. Spock eventually engineered their rescue. 
Dammit, I thought I might be the first one to get Monument …
The last episode of the incredibly awful Space Rangers has one of the eponymous Rangers on trial for a murder he didn’t commit.
One episode of Gerry Anderson’s UFO was titled (aptly) “Court Martial”, with SHADO Colonel Paul Foster on trial for espionage.
And there was that particularly harrowing episode of Terry Nation’s Survivors called “Law and Order”, in which the small community of plague survivors have to deal with the aftermath of a murder.
(And, with regard to Data’s trial - isn’t the question of whether or not an entity is legally a “person”, one that you should probably settle before you give said entity a commission in the flippin’ military? If Data is a Starfleet officer, he has all therights and responsibilities thereof - end of discussion.)
In The Transformers: The Movie, both Kup and Hot Rod were put on trial by the Quintessons. They were judged “Innocent” and then sent to their doom to the hungry Sharkticons below.
They escaped.
I can’t recall if it was in I, Robot or was one of the other robot stories, but there was a court scene in Galley Slave, in which a professor accuses a robot editor of intentionally inserting errors into his latest book.
Going back to Star Trek, Kirk vs. The Gorn was a sort of trial.
Also, there was a Klingon trial in a Next Generation episode, in which Worf is put on trial for something his father was accused of. It was a good story, because Worf knew his accuser’s father had actually done it, but he let himself lose the trial to protect his brother and the Klingon-Federation alliance. In a later episode, Worf gives the accuser a terminal case of Bat’leth poisoning (in response for other nasty things this guy did). The accuser’s sisters are disposed of in one of the movies, which rather fittingly ended the original traitor’s bloodline. Klingons love stories like that.
[Actually, I think I now remember an episode in which Duras has a son, who petitions a Klingon court to restore his families honor. He didn’t win. Don’t recall the kid being offed, so I suppose there may be one dishonored soul left in the family.]
I’m just glad I’m not the only one here to have read it! Biggle doesn’t show up on a lot of lists, but I’ve always liked him.