The key here, for most of the people, is Arya's prayer in Arya VI, ACOK.
Arya watched and listened and polished her hates the way Gendry had
once polished his horned helm. Dunsen wore those bull’s horns now,
and she hated him for it. She hated Polliver for Needle, and she
hated old Chiswyck who thought he was funny. And Raff the
Sweetling, who’d driven his spear through Lommy’s throat, she hated
even more. She hated Ser Amory Lorch for Yoren, and she hated
Ser Meryn Trant for Syrio, the Hound for killing the butcher’s boy Mycah, and Ser Ilyn and Prince Joffrey and the queen for the
sake of her father and Fat Tom and Desmond and the rest, and even for
Lady, Sansa’s wolf. The Tickler was almost too scary to hate. At
times she could almost forget he was still with them; when he was not
asking questions, he was just another soldier, quieter than most, with
a face like a thousand other men.
Every night Arya would say their names. “Ser Gregor,” she’d whisper to
her stone pillow. “Dunsen, Polliver, Chiswyck, Raff the Sweetling. The
Tickler and the Hound. Ser Amory, Ser Ilyn, Ser Meryn, King Joffrey,
ACOK - Arya VI
Joffrey I Baratheon
He got a spot because of the execution of Eddard Stark along with murder of Winterfell retinue that came to King's Landing with Eddard and Lady's execution due to Cersei's insistence and Joffrey's lies.
The Wiki says Arya added him to his list when she heard him joke about a gangrape they committed in an inn. That is wrong. Arya did not learn about that until she overheard him ACOK Arya VII. Not to mention, Arya was not Weese's charge till Arya VII (or more precisely VI's end).
Weese saw that they were well supplied with drink. “They always have a
good thirst, that lot,” he grumbled. “Weasel, go up and ask if they’ve
got any clothes that need mending, I’ll have the women see to it.”
Arya ran up her well-scrubbed steps. No one paid her any mind when she
entered. Chiswyck was seated by the fire with a horn of ale to hand,
telling one of his funny stories. She dared not interrupt, unless she
wanted a bloody lip.
“After the Hand’s tourney, it were, before the war come,” Chiswyck was
saying. “We were on our ways back west, seven of us with Ser Gregor.
Raff was with me, and young Joss Stilwood, he’d squired for Ser in the
lists. Well, we come on this pisswater river, running high on account
there’d been rains. No way to ford, but there’s an alehouse near, so
there we repair. Ser rousts the brewer and tells him to keep our horns
full till the waters fall, and you should see the man’s pig eyes shine
at the sight o’ silver. So he’s fetching us ale, him and his daughter,
and poor thin stuff it is, no more’n brown piss, which don’t make me
any happier, nor Ser neither. And all the time this brewer’s saying
how glad he is to have us, custom being slow on account o’ them rains.
The fool won’t shut his yap, not him, though Ser is saying not a word,
just brooding on the Knight o’ Pansies and that bugger’s trick he
played. You can see how tight his mouth sits, so me and the other lads
we know better’n to say a squeak to him, but this brewer he’s got to
talk, he even asks how m’lord fared in the jousting. Ser just gave him
this look.” Chiswyck cackled, quaffed his ale, and wiped the foam away
with the back of his hand. “Meanwhile, this daughter of his has been
fetching and pouring, a fat little thing, eighteen or so-”
“Thirteen, more like,” Raff the Sweetling drawled.
“Well, be that as it may, she’s not much to look at, but Eggon’s been
drinking and gets to touching her, and might be I did a little
touching meself, and Raff’s telling young Stilwood that he ought to
drag the girl upstairs and make hisself a man, giving the lad courage
as it were. Finally Joss reaches up under her skirt, and she shrieks
and drops her flagon and goes running off to the kitchen. Well, it
would have ended right there, only what does the old fool do but he
goes to Ser and asks him to make us leave the girl alone, him being an
anointed knight and all such.
“Ser Gregor, he wasn’t paying no mind to none of our fun, but now he
looks, you know how he does, and he commands that the girl be brought
before him. Now the old man has to drag her out of the kitchen, and no
one to blame but hisself. Ser looks her over and says, ‘So this is the
whore you’re so concerned for’ and this besotted old fool says, ‘My
Layna’s no whore, ser’ right to Gregor’s face. Ser, he never blinks,
just says, ‘She is now’ tosses the old man another silver, rips the
dress off the wench, and takes her right there on the table in front
of her da, her flopping and wiggling like a rabbit and making these
noises. The look on the old man’s face, I laughed so hard ale was
coming out me nose. Then this boy hears the noise, the son I figure,
and comes rushing up from the cellar, so Raff has to stick a dirk in
his belly. By then Ser’s done, so he goes back to his drinking and we
all have a turn. Tobbot, you know how he is, he flops her over and
goes in the back way. The girl was done fighting by the time I had
her, maybe she’d decided she liked it after all, though to tell the
truth I wouldn’t have minded a little wiggling. And now here’s the
best bit... when it’s all done, Ser tells the old man that he wants
his change. The girl wasn’t worth a silver, he says... and damned if
that old man didn’t fetch a fistful of coppers, beg mlord’s pardon,
and thank him for the custom!” The men all roared, none louder than
Chiswyck himself, who laughed so hard at his own story that snot
dribbled from his nose down into his scraggy grey beard.
ACOK - Arya VII
In Arya VI, she had already added him to her list as evident by the key quotation above.
The reason she gave was that she hated his attempts at humour without explicitly describing exactly what sort of jokes was he making. My guess is it was some jokes he made about torture of the villagers by the Tickler.
“Tickler makes them howl so hard they piss themselves,” old stoop- shoulder Chiswyck told them. [...] she hated old Chiswyck who thought he was funny
ACOK - Arya VI
Ser Gregor Clegane
The wiki says it was because he captured Arya and her friends. But I can't find any reference for this. She never explicitly mentions it. An educated guess would be that it was presumably because he chose the victims to be tortured and killed people indiscriminately. He gave her plenty of reasons to be added to the list.
The Mountain would come into the storehouse after he had broken his
fast and pick one of the prisoners for questioning. The village folk
would never look at him. Maybe they thought that if they did not
notice him, he would not notice them... but he saw them anyway and
picked whom he liked. There was no place to hide, no tricks to play,
no way to be safe.
One girl shared a soldier’s bed three nights running; the Mountain
picked her on the fourth day, and the soldier said nothing.
A smiley old man mended their clothing and babbled about his son, off
serving in the gold cloaks at King’s Landing. “A king’s man, he is,”
he would say, “a good king’s man like me, all for Joffrey.” He said it
so often the other captives began to call him All-for-Joffrey whenever
the guards weren’t listening. All-for-Joffrey was picked on the fifth
day. A young mother with a pox-scarred face offered to freely tell
them all she knew if they’d promise not to hurt her daughter. The
Mountain heard her out; the next morning he picked her daughter, to be
certain she’d held nothing back.
The ones chosen were questioned in full view of the other captives, so
they could see the fate of rebels and traitors.
One girl, prettier than the others, was made to go with four or five
different men every night, until finally she hit one with a rock. Ser
Gregor made everyone watch while he took off her head with a sweep of
his massive two-handed greatsword. “Leave the body for the wolves,” he
commanded when the deed was done, handing the sword to his squire to
ACOK - Arya VI
So it could be either one or a mixture of all these events that landed him on the list.
That one is simple. It's because he killed Mycah, the butcher boy died because of Joffrey's lies.
He stole Gendry's helmet, an almost negligible crime compared to what the rest of them did.
Same reasons as her son's.
He killed Yoren.
Same reasons as Cersei and Joffrey.
For stealing needle. Another comparatively negligible offense.
Raff the Sweetling
For murdering Lommy.
Ser Meryn Trant
For killing Syrio Forel.
Similar case to Gregor's. He abused Arya and the other captives on a number of occasions, starting from the day she was assigned to his workforce.
In his own small strutting way, Weese was nearly as scary as Ser
Gregor. The Mountain swatted men like flies, but most of the time he
did not even seem to know the fly was there. Weese always knew you
were there, and what you were doing, and sometimes what you were
thinking. He would hit at the slightest provocation, and he had a dog
who was near as bad as he was, an ugly spotted bitch that smelled
worse than any dog Arya had ever known. Once she saw him set the dog
on a latrine boy who’d annoyed him. She tore a big chunk out of the
boy’s calf while Weese laughed.
It took him only three days to earn the place of honor in her nightly prayers. “Weese,” she would whisper, first of all. “Dunsen,
Chiswyck, Polliver, Raff the Sweetling. The Tickler and the Hound. Ser
Gregor, Ser Amory, Ser Ilyn, Ser Meryn, King Joffrey, Queen Cersei.”
ACOK - Arya VII
Presumably because he tortured the prisoners brutally.
Members of House Frey
She doesn't exactly know the names of the Freys involved in Red Wedding, which is why she didn't formally add them to her list. She does however intend to kill them all.
Each night before sleep, she murmured her prayer into her pillow. “Ser
Gregor,” it went. “Dunsen, Raff the Sweetling, Ser Ilyn, Ser Meryn,
Queen Cersei.” She would have whispered the names of the Freys of
the Crossing too, if she had known them. One day I’ll know, she told
herself, and then I’ll kill them all.
AFFC - Arya II