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I was re-reading the books and came across these passages:

Once, Aunt Petunia, tired of Harry coming back from the barber’s looking as though he hadn’t been at all, had taken a pair of kitchen scissors and cut his hair so short he was almost bald except for his fringe, which she left ‘to hide that horrible scar’.... Next morning, however, he had got up to find his hair exactly as it had been before Aunt Petunia had sheared it off.

Another time, Aunt Petunia had been trying to force him into a revolting old jumper of Dudley’s (brown with orange bobbles). The harder she tried to pull it over his head, the smaller it seemed to become, until finally it might have fitted a glove puppet, but certainly wouldn’t fit Harry.

On the other hand, he’d got into terrible trouble for being found on the roof of the school kitchens. Dudley’s gang had been chasing him as usual when, as much to Harry’s surprise as anyone else’s, there he was sitting on the chimney.

Harry sat up and gasped; the glass front of the boa constrictor’s tank had vanished.

So Harry's done Apparation, some vanishing spell, and transfiguration (with the old jumper) accidentally before he ever went to Hogwarts. Why doesn't accidental magic seem to happen around Hogwarts?

Answering 'Why doesn't accidental magic seem to happen around Hogwarts?', it does - but wizards learn to control it, which means that less accidents happen.

Here are some examples through the series - mainly later on too, after they had been learning for a while:

In Half Blood Prince, Ron accidentally makes it snow, then explodes a flask full of vinegar. Harry freezes his.

“Ron, you’re making it snow,” said Hermione patiently, grabbing his wrist and redirecting his wand away from the ceiling from which, sure enough, large white flakes had started to fall.

Later on,

“Now, now, boys,” squeaked Professor Flitwick reproachfully. “A little less talk, a little more
action… Let me see you try…”

Together they raised their wands, concentrating with all their might, and pointed them at their flasks. Harry’s vinegar turned to ice; Rons flask exploded.

The OWL exams are also another source of accidental magic - Hannah Abbot accidentally turns a ferret into a flock of flamingos:

poor Hannah Abbott lost her head completely at the next table and somehow managed to multiply her ferret into a flock of flamingos, causing the examination to be halted for ten minutes while the birds were captured and carried out of the Hall.

And Ron turns a plate into a mushroom:

Ron had caused a dinner plate to mutate into a large mushroom and had no idea how it had happened.

Older wizards do still perform accidental magic - sparks fly from Scrimgeour's wand in the Deathly Hallows, and a thin stream of fire comes from Bellatrix's.