I can think of plenty of examples. In the spirit of TGnat’s answer, I’ve compiled a list of Muggle offences of which Dumbledore is guilty (which are probably offences in the magical world as well).
Everything I list below has a good motivation on Dumbledore’s part – I’m not saying whether these are right or wrong, just that they are instances where Dumbledore may have broken wizarding law. (I’m also not saying you could get a successful prosecution!)
Perverting the course of justice
In Prisoner of Azkaban, Dumbledore gives Harry and Hermione detailed instructions for finding Sirius, and suggests that they free Buckbeak as well:
“Now, pay attention,” said Dumbledore, speaking very low, and very clearly. “Sirius is locked in Professor Flitwick’s office on the seventh
floor. Thirteenth window from the right of the West Tower. If all goes well, you will be able to save more than one innocent life tonight. But remember this, both of you: you must not be seen. Miss Granger, you know the law — you know what is at stake…. You — must — not — be — seen.”
Putting aside the question of whether either of them are “truly” guilty, they have been tried in a Ministry court and found guilty. Dumbledore can’t take all of the blame, but he is responsible for incitement. (Which was still an offence in England and Wales in ~1993/PoA.)
After he escapes, Sirius is still a wanted man. Dumbledore knows his whereabouts, but does not tell the Ministry. I assume he doesn’t tell them that Sirius is an unregistered Animagus, either.1 In fact, we know that Kingsley Shacklebolt deliberately mislead the Ministry search:
[Arthur Weasley:] “Kingsley Shacklebolt’s been a real asset, too; he’s in charge of the hunt for Sirius, so he’s been feeding the Ministry information that Sirius is in Tibet.”
If he was doing so on Dumbledore’s orders, then that’s another charge of incitement.
Further, Dumbledore fails to inform the Ministry that Peter Pettigrew is alive. As a key witness at the Black massacre, and an apparently dead man, the Ministry might want to talk to him.
In the same vein, when he claims credit for Dumbledore’s Army in Order of the Phoenix, he is drawing attention from the true “criminals” – Harry and Hermione.
When the Ministry officials arrive to arrest him in OotP, he explicitly says that he won’t be coming. That sounds illegal. He then threatens Dawlish, who has come to arrest him:
“Don’t be silly, Dawlish,” said Dumbledore kindly. “I’m sure you are an excellent Auror - I seem to remember that you achieved ‘Outstanding’ in all your NEWT s — but if you attempt to — er — bring me in by force, I will have to hurt you.”
At a stretch, this might qualify as criminal threatening or intimidation.
As the headmaster of Hogwarts, he has a duty of care to his students.
In Half-Blood Prince, he is aware that Draco Malfoy is plotting to kill him, but does not stop Malfoy from trying. Along the way, Katie, Ron and Madam Rosmerta2 are injured, and somebody could have been killed if he didn’t stop Malfoy.
Although they all made a full recovery, this is still negligence. (The crime is failing to exercise due care, not the eventual effect.)
There are other instances where Hogwarts is distinctly unsafe for students, or where Dumbledore fails to act in a “reasonable” way – I just picked that one because it’s the most extreme.
1 I’m not suggesting the Ministry would be interested in prosecuting Sirius for being an unregistered Animagus, but it would be useful for them to know – it explains his Azkaban escape, and how he can evade the Dementors.
2 Under the influence of the Imperius curse.