Crookshanks is Hermione's familiar in PoA, GoF, and OOTP. I cannot recall mention of Crookshanks following OOTP, though. What happened to Crookshanks? Does canon refer to Crookshanks in either HBP or DH?
In the Deathly Hallows when Harry is dismissed from helping Mr. Weasley with weeding the garden he goes upstairs to look for Ron. When he enters the room, Ron is cleaning and Hermione is sitting in the corner with Crookshanks organizing books.
Since they had to leave during the wedding reception in a hurry, it is presumed that Crookshanks remained at the Burrow until they returned after the Second Wizarding War.
Crookshanks gets a few mentions in subsequent books. (Living in a world with Harry Potter ebooks makes this ~much easier to check.)
Hermione takes Crookshanks to Hogwarts, as per previous years.
We first see him when Harry arrives at the Burrow:
As Harry sat down, a furry ginger cat with a squashed face lumped onto his knees and settled there, purring.
“So Hermione's here?” he asked happily as he tickled Crookshanks behind the ears.
“Oh yes, she arrived the day before yesterday,” said Mrs. Weasley, rapping a large iron pot with her wand. […]
“Night, Mr. Weasley,” said Harry, pushing back his chair. Crookshanks leapt lightly from his lap and slunk out of the room.
— Chapter 5, An Excess of Phlegm
Later, we see Crookshanks accompanying the other pets to Hogwarts:
And in fact, their departure the following morning was smoother than usual. The Ministry cars glided up to the front of the Burrow to find them waiting, trunks packed; Hermione's cat, Crookshanks, safely enclosed in his traveling basket; and Hedwig; Ron's owl, Pig-widgeon; and Ginny's new purple Pygmy Puff, Arnold, in cages.
— Chapter 7, The Slug Club
We encounter Crookshanks three more times in the book: when he’s getting annoyed at a Fanged Frisbee flying around the Gryffindor Common Room, and then when he has murderous intentions towards Arnold:
Ron looked a little uncomfortable and began playing with the Fanged Frisbee Hermione had taken from the fourth-year student. It zoomed around the common room, snarling and attempting to take bites of the tapestry. Crookshanks's yellow eyes followed it and he hissed when it came too close.
— Chapter 9, The Half-Blood Prince
As he was ducking toward the drinks table, he walked straight into Ginny, Arnold the Pygmy Puff riding on her shoulder and Crookshanks mewing hopefully at her heels. […]
She patted him on the arm; Harry felt a swooping sensation in his stomach, but then she walked off to help herself to more butterbeer. Crookshanks trotted after her, his yellow eyes fixed upon Arnold.
— Chapter 14, Felix Felicis
He isn’t mentioned again in this book. Presumably Hermione takes him home with her at the end of the school year, as she would have done in previous years. Nothing too unusual here.
Hermione leaves Crookshanks at the Burrow.
When Harry’s at the Burrow, he finds Crookshanks alongside Hermione. Presumably she had to take him with her when she left her parents, because a half-Kneazle would have aroused suspicion among her parents, especially since they think they’re Muggles.
The room was just as messy as it had been all week; the only change was that Hermione was now sitting in the far corner, her fluffy ginger cat, Crookshanks, at her feet, sorting books, some of which Harry recognized as his own, into two enormous piles.
— Chapter 6, The Ghoul in Pyjamas
He shows up once more in the chapter, when he gets under everybody’s feet (that must be the half-cat side of him coming out). Canon doesn’t tell us what happens to him after that.
Later in the book, Ron makes a flippant reference to Crookshanks (when trying to work out how to reach the knot on the Whomping Willow), but we don’t see Crookshanks the animal again in the book.
There's nothing from Canon and I can't find a statement from J.K. Rowling. There's certainly a lot of sites on the web asking the same question, and even a Facebook page. I did find this from harrypotter.wikia.com:
During the height of the Second Wizarding War, Hermione and Crookshanks came to stay at the Burrow, but Hermione left with Harry and Ron after Bill Weasley and Fleur Delacour's wedding reception was interrupted by Death Eaters. It is unknown what happened to Crookshanks while Hermione was searching for Horcruxes; most likely, he stayed in the Weasley's care, given Ginny's fondness of cats. Alternately, he may have left the Weasley household alone.