In HPSP when she stepped up for Ron and Harry after they saved her from the troll.
"Please, Professor McGonagall - they were looking for me."
Hermione had managed to get to her feet at last.
"I went looking for the troll because I - I thought I could deal with it on my own - you know, because I've read all about them." Ron dropped his wand. Hermione Granger telling a downright lie?
When she was the first one to realise who had paralysed all the students in HP2 with her incredible wits and her can-do attitude and saved not only her life but presumably that of many other muggle-born-students at Hogwarts.
And beneath this, a single word had been written, in a hand Harry recognised as Hermione's. Pipes.
It was as though somebody had just flicked a light on in his brain.
"Ron", he breathed, "this is it. This is the answer. The monster in the Chamber's a Basilisk - a giant serpent! That's why I've been hearing that voice all over the place, and nobody else has heard it..."
...and Hermione and that Ravenclaw Prefect were found with a mirror next to them. Hermione had just realised the monster was a basilisk. I bet you anything she warned the first person she met to look round corners with a mirror first!"
When she smacked Draco Malfoy for not only lying about Buckbeak hurting him, but also sneering at Hagrid for being inconsolable about the looming execution of his beloved hippogriff.
"Look at him blubber!"
Malfoy, Crabbe and Goyle had been standing just inside the castle doors, listening.
"Have you ever seen anything quite as pathetic?" said Malfoy. "And he's supposed to be our teacher!"
Harry and Ron both made furious moves towards Malfoy, but Hermione got there first - SMACK!
She had slapped Malfoy around the face with all her strength she could muster. Harry, Ron, Crabbe and Goyle stood flabbergasted as Hermione raised her hand again.
"Don't you dare call Hagrid pathetic, you foul - you evil-"
"Hermione!" said Ron weakly, and he tried to grab her hand as she swung it back.
"Get off, Ron!"
Hermione pulled out her wand. Malfoy stepped backwards.
When she stormed out of Trelawney's classroom after the latter only talking nonsense. For the first time, Hermione challenged a teacher and decided to not take any more nonsense, which proves she isn't a teacher's pet or sucker-up but simply a genuinely interested student with great aptitude and passion.
"It is here, plainer than ever before ... my dear, stalking towards you, growing ever closer ... The Gr-"
"Oh for goodness sake!" said Hermione, loudly. "Not that ridiculous Grim again."
Professor Trelawney raised her enormous eyes to Hermione's face. (...)
"I am sorry to say that from the moment you have arrived in this class, my dear, it has been apparent that you do not have what the noble art of Divination requires. Indeed, I don't remember ever meeting a student whose mind was so hopelessly Mundane."
There was a moment of silence. Then -
"Fine!" said Hermione suddenly, getting up and cramming Unfogging the Future back into her bag. "Fine!" she repeated, swinging her bag over her shoulder and almost knocking Ron off his chair. "I give up! I'm leaving!"
When she founded S.P.E.W and stood up for elf rights and stood with her principles, even though her people to be deliberated needed some convincing themselves...
‘What’s in the box?’ he asked, pointing at it.
‘Funny you should ask,’ said Hermione, with a nasty look at Ron. She took off the lid, and showed them the contents. Inside were about fifty badges, all of different colours, but all bearing the same letters: S.P.E.W.
‘“Spew”?’ said Harry, picking up a badge and looking at it. ‘What’s this about?’
‘Not spew,’ said Hermione impatiently. ‘It’s S – P – E – W. Stands for the Society for the Promotion of Elfish Welfare.’
‘Never heard of it,’ said Ron.
‘Well, of course you haven’t,’ said Hermione briskly, ‘I’ve only just started it.’
‘Yeah?’ said Ron in mild surprise. ‘How many members have you got?’
‘Well – if you two join – three,’ said Hermione.
‘And you think we want to walk around wearing badges saying “spew”, do you?’ said Ron.
‘S – P – E – W!’ said Hermione hotly. ‘I was going to put Stop the Outrageous Abuse of Our Fellow Magical Creatures and Campaign for a Change in Their Legal Status – but it wouldn’t fit. So that’s the heading of our manifesto.’
When she figured out Rita Skeeter's dirty little secret and outwitted her, as only a Hermione Granger can do and finally put a rest to Rita's foul mouth.
"Oh not electronic bugs", said Hermione. "No, you see...Rita Skeeter" - Hermione's voice trembled with quiet triumph - "is an unregistered Animagus. She can turn-"
Hermione pulled a small sealed glass jar out of her bag.
"-into a beetle."
"You're kidding", said Ron. "You haven't ... she's not ..."
"Oh yes, she is", said Hermione happily, brandishing the jar at them.
"Look very closely, and you'll notice the markings around her antennae are exactly like those foul glasses she wears."
When she urged Harry to found and lead the DA, once more proving she is not a student who would give her dedication to any teacher, as a teacher's pet would do, but puts her own principles and beliefs over being a flawless student and encouraging other to do so, too.
"Well, learn Defence Against the Dark Arts ourselves", said Hermione.
"We can't do much by ourselves", said Ron in a defeated voice. "I mean, all right, we can go and look jinxes up in the library and try and practise them, I suppose-"
"No (...) we need a teacher, a proper one who can show us how to handle spells and correct us if we're going wrong."
"If you're talking about Lupin...", Harry began.
"No, no, I'm not talking about Lupin", said Hermione.
"Who, then?" said Harry, frowning at her.
(...) "Isn't it obvious?" she said. "I'm talking about you, Harry."
It is probably not one of her best, but she makes me laugh so hard, every time I read the part. This is in HP6 when Ron is warming up to Lavender Brown and Hermione decides to get back at him by asking out Cormac McLaggen (and she had to pay bitterly for the sweetness of revenge). She's at the table with the two gossips Parvati Patil and Lavender Brown, behaving all girly, proving that she has not only mastered books and being a self-confident woman, but understands and can play with the gigglish, silly worlds of girls, getting an advantage out for herself. Hermione, Hermione, is there anything you can't do?
"Hi Parvati!" said Hermione, completely ignoring Ron and Lavender. "Are you going to Slughhorn's party tonight?"
"No invite", Parvati said gloomily. "I'd love to go, though, it sounds like it's going to be really good...you're going, aren't you?"
"Yes, I'm meeting Cormac at eight and we're-"
There was a noise like a plunger being withdrawn from a blicked sink and Ron surfaced. Hermione acted as though she had not seen or heard anything.
"-we're going up to the party together."
"Cormac?" said Parvati. (...)
"That's right", said Hermione sweetly. "The one who almost", she put a great deal of emphasis on the word, "became Gryffindor Keeper."
"Are you going out with him, then?" asked Parvati, wide-eyed.
"Oh - yes - didn't you know?", said Hermione, with a most un-Hermione-ish giggle.
And of course, finally, I have to include this moment of Hermione kick-assness among those many, many moments where she shined. In the Battle of Hogwarts and the very end of the last book (sniff, sniff), she finally manages to do what Ron never was able to do and after having endured their sexually loaded bickering since book 4, we finally come to the point where Hermione steers it into a new direction and gets her guy. I hope Ron knows what a magnificent woman he's netted himself...
"Hang on a moment", said Ron sharply. "We've forgotten someone!"
"Who?" asked Hermione.
"The house-elves, they'll all be down in the kitchen, won't they?"
"You mean we ought to get them fighting?" asked Harry.
"No", said Ron seriously. "I mean we should tell them to get out. We don't want any more Dobbys, do we? We can't order them to die for us-"
There was a clatter as the Basilisk fangs cascaded out of Hermione's arms. Running at Ron, she flung them around his neck and kissed him full on the mouth. Ron threw away the fangs and broomstick he was holding and responded with such enthusiasm that he lifted Hermione off her feet.
"Is this the moment?" Harry asked weakly (...).
Ron and Hermione broke apart, their arms still around each other.
"I know, mate", said Ron, who looked as though he had recently been hit on the back by a Bludger, "so it's now or never, isn't it?"