Crimes that can get an Azkaban sentence are certainly not limited to being involved with Dark wizards.
Crimes that get time in Azkaban without needing Dark wizards:
Letting a creature attack students at Hogwarts.
“They think, up at the school, that Hagrid’s been setting a – a – something on students. They’ve taken him to Azkaban.”
- Harry Potter and the Chamber of Secrets, Chapter 15 (Aragog)
Using any of the three Unforgivable Curses.
Using any of the three Unforgivable Curses is in itself enough to get a life sentence in Azkaban, even if they weren’t used by someone who was or was connected with a Dark wizard. Simply using one of them on someone is enough.
“Now … those three curses – Avada Kedavra, Imperius and Cruciatus – are known as the Unforgivable Curses. The use of any one of them on a fellow human being is enough to earn a life sentence in Azkaban.”
- Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
Defying the Ministry of Magic.
Arthur Weasley, who would know this kind of thing as a Ministry employee, says Dumbledore could get himself thrown in Azkaban for defying the Ministry if he keeps it up.
“But Dumbledore says he doesn’t care what they do as long as they don’t take him off the Chocolate Frog Cards,’ said Bill, grinning.
‘It’s no laughing matter,’ said Mr Weasley sharply. ‘If he carries on defying the Ministry like this he could end up in Azkaban, and the last thing we want is to have Dumbledore locked up.”
- Harry Potter and the Order of the Phoenix, Chapter 5 (The Order of the Phoenix)
Trespassing and attempted robbery at the Ministry of Magic.
Sturgis Podmore was convicted and sentenced to Azkaban for trespassing and attempted robbery. The article in the Daily Prophet says he was convicted on both charges, meaning both trespassing and attempted robbery are charges that can earn jail time.
“Sturgis Podmore, 38, of number two, Laburnum Gardens, Clapham, has appeared in front of the Wizengamot charged with trespass and attempted robbery at the Ministry of Magic on 31st August. Podmore was arrested by Ministry of Magic watchwizard Eric Munch, who found him attempting to force his way through a top-security door at one o’clock in the morning. Podmore, who refused to speak in his own defence, was convicted on both charges and sentenced to six months in Azkaban.”
- Harry Potter and the Order of the Phoenix, Chapter 14 (Percy and Padfoot)
Enchanting items which would be used by Muggles.
Willy Widdershins was arrested for enchanting toilets to explode, though he was able to get out of the charge by giving Umbridge information on Harry.
“I was just reading about Willy Widdershins’s arrest when you arrived. You know Willy turned out to be behind those regurgitating toilets back in the summer? One of his jinxes backfired, the toilet exploded and they found him lying unconscious in the wreckage covered from head to foot in –”
- Harry Potter and the Order of the Phoenix, Chapter 22 (St Mungo’s Hospital for Magical Maladies and Injuries)
However, he was caught committing another crime - selling Muggles biting doorknobs.
“George, be quiet!’ snapped Mrs Weasley.
‘Anyway,’ said Mr Weasley, in a raised voice, ‘this time Willy’s been caught selling biting doorknobs to Muggles and I don’t think he’ll be able to worm his way out of it because, according to this article, two Muggles have lost fingers and are now in St Mungo’s for emergency bone re-growth and memory modification. Just think of it, Muggles in St Mungo’s! I wonder which ward they’re in?”
- Harry Potter and the Order of the Phoenix, Chapter 22 (St Mungo’s Hospital for Magical Maladies and Injuries)
Attacking Muggles, as well as attacking Ministry officials.
Morfin and Marvolo Gaunt were both charged with attacking Muggles. Marvolo got a longer sentence because he’d also injured Ministry employees while attempting to evade capture.
“Ogden Apparated back to the Ministry and returned with reinforcements within fifteen minutes. Morfin and his father attempted to fight, but both were overpowered, removed from the cottage and subsequently convicted by the Wizengamot. Morfin, who already had a record of Muggle attacks, was sentenced to three years in Azkaban. Marvolo, who had injured several Ministry employees in addition to Ogden, received six months.”
- Harry Potter and the Half-Blood Prince, Chapter 10 (The House of Gaunt)
Percival Dumbledore is also sentenced to Azkaban for attacking Muggles.
“Scarcely a year previously, his father, Percival, had been convicted of a savage and well-publicised attack upon three young Muggles.
Albus never attempted to deny that his father (who was to die in Azkaban) had committed this crime; on the contrary, when I plucked up courage to ask him, he assured me that he knew his father to be guilty.”
- Harry Potter and the Deathly Hallows, Chapter 2 (In Memoriam)
Murdering Muggles.
Morfin was arrested for murdering Muggles, and sent to Azkaban.
“So the Ministry called upon Morfin. They did not need to question him, to use Veritaserum or Legilimency. He admitted to the murder on the spot, giving details only the murderer could know. He was proud, he said, to have killed the Muggles, had been awaiting his chance all these years. He handed over his wand, which was proved at once to have been used to kill the Riddles. And he permitted himself to be led off to Azkaban without a fight.”
- Harry Potter and the Half-Blood Prince, Chapter 17 (A Sluggish Memory)
Burglary (and possibly impersonating an Inferius).
Mundungus Fletcher was sent to Azkaban for attempting a burglary while impersonating an Inferius. It’s unclear if his Inferius impression worsened his crime, or if it was just an additional detail.
“Yes!’ said Hermione, causing both Harry and Ron to gag on their breakfast, ‘but it’s all right, he’s not dead – it’s Mundungus, he’s been arrested and sent to Azkaban! Something to do with impersonating an Inferius during an attempted burglary …” - Harry Potter and the Half-Blood Prince, Chapter 21 (The Unknowable Room)*
Using accidental underage magic isn’t enough to be sent to Azkaban.
“I broke the law!’ Harry said. ‘The Decree for the Restriction of Underage Wizardry!’
‘Oh, my dear boy, we’re not going to punish you for a little thing like that!’ cried Fudge, waving his crumpet impatiently. ‘It was an accident! We don’t send people to Azkaban just for blowing up their aunts!”
- Harry Potter and the Prisoner of Azkaban, Chapter 3 (The Knight Bus)