Sirius Black is Harry Potter's godfather and the closest thing he ever gets to a real parent. Unfortunately, Sirius spends the majority of Harry's childhood imprisoned in Azkaban, thanks to Peter Pettigrew. When Sirius finally escapes in The Prisoner of Azkaban he does his best to make up for lost time. He tries to be the father figure Harry desperately wants and needs. Whether he succeeds is another matter.
There's no doubt Sirius loved Harry. However, Sirius had also been through a lot of trauma and he wasn't always the most reliable or stable figure in Harry's life. We're looking at five times Sirius fulfilled his role as godfather, and five times he probably should have left well enough alone.
Not So Great: Trusted Peter Pettigrew
Now you might argue that Sirius had no way to know Pettigrew planned to betray the Potters. All the Marauders trusted each other with their lives. There was no reason to suspect that Peter was any different. However, this is less about Sirius trusting Peter than about him not trusting himself.
Lily and James originally wanted to make Sirius the Secret-Keeper for their Fidelius Charm. But Sirius worried that his family's connections to the Death Eaters would make him a target, and encouraged them to choose Peter instead. Tragically, this led to the Potters' death when Pettigrew betrayed them to the Dark Lord. Sirius certainly wouldn't have given them up so easily, as he says himself he would have rather died that betrayed his friends.
Great: Gave Harry His Broom
It would be hard not to notice that Harry was kind of a star on the Gryffindor Quidditch team, and it was a blow when his Nimbus 2000 was destroyed by the Whomping Willow. Lucky for him, he received an anonymous gift by mail that was revealed to be a Firebolt, a broom Harry had desperately wanted ever since seeing it in Diagon Alley.
Unbeknownst to Harry, the broom was a present from his godfather. At the time, the professors at Hogwarts were afraid that the broom might have been tampered with and was thus dangerous, so he wasn't able to immediately use it. Eventually it came back clean and Harry could go back to being a prodigy Seeker. Did you know: Sirius also gave Harry his very first broomstick when he was just one year old.
Not So Great: Broke Ron's Leg
The Prisoner of Azkaban was a difficult time for everyone, particularly Sirius. He had just broken out of prison and was on the razor's edge of sanity. He was obsessed with finding and killing Wormtail in order to protect Harry. To this end, he transformed into a dog and attacked Ron (who was carrying Scabbers). Sirius dragged him bodily into the roots of the Whomping Willow, breaking his leg. It's really not a good look when your legal guardian physically attacks your best friend.
Great: Signed His Hogsmeade Permission Form
Third year Hogswarts students are allowed to visit the nearby village of Hogsmeade on weekends. However, you need a guardian's permission and Harry doesn't have the best guardians. He blew his chance to convince Mr. Dursley to sign the form when he accidentally inflated his Aunt Marge.
After spending all of his third year sneaking into Hogsmeade using hidden passages and his Invisibility Cloak, Harry finally caught a break over the summer between third and fourth year. Sirius sent him a signed note giving him permission to visit Hogsmeade. Since Sirius is wanted for murder, this might not have flown at a normal school, but we all know Dumbledore's not really a stickler for rules.
Not So Great: Risked His Life For No Reason
Sirius could be extremely reckless at times. One example is at the beginning of The Order of the Phoenix, when he leaves Grimmauld Place to see Harry off at King's Cross Station. He disguises himself as Padfoot, so he at least makes some effort to hide his appearance. But he's still a wanted murderer at this point. If anyone had recognized him, it could have gotten very bad very fast. In fact, Malfoy did recognize him and made snide comments to Harry about it. Luckily nothing much came of it, but it's Sirius' job to try to protect Harry, not put them both in danger.
Great: Protected The Trio From Lupin
After the Marauders reunion in the Shrieking Shack, where Pettigrew's true form was revealed, things were finally looking up. With the real murderer in hand, Sirius could clear his name. He reconciled with one of his best friends, Lupin. He could take true guardianship of Harry and give him a loving home firs the first time.
Unfortunately, it was not to be. In all the excitement, Lupin lost track of the cycle of the moon and began to turn into a werewolf. Sirius shifted into his Animagus form to distract Lupin and give Harry and his friends a chance to escape. This also had the side effect of giving Pettigrew a chance to escape too. Regardless, Sirius risked himself to save Harry, like a good godfather should.
Not So Great: Treated Harry Like He Was James
Many of the adults in Harry's life were of the opinion that Sirius wouldn't actually be the best father figure for Harry. This is partially because that Sirius tended to treat Harry the same way he might have treated his best friend James. Sirius was imprisoned immediately after James' death and almost lost his mind in Azkaban, so his perspective is a little skewed. But Harry was a child and Sirius was still quick to encourage him to take risky moves, such as form Dumbledore's Army, when most guardians would have been more concerned for his safety.
Great: Fought For Him In The Department of Mysteries
Harry was lured to the Department of Mysteries following a fake vision of Sirius being tortured there. Determined to rescue his godfather, he instead walked himself and his friends into a Death Eater ambush. Of course, one Sirius found out about this, he rushed to Harry's aid alongside other members of the Order.
Ironically, it was Sirius that ended up saving Harry instead of the opposite. In particular, he stopped Death Eater Antonin Dolohov from cursing Harry. Shortly after, he loses his life in a duel with Bellatrix Lestrange, but he went down defending his godson.
Not So Great: Is Kind Of A Hypocrite
Sirius is quick to give Harry advice and, more often than not, it's good advice. But he doesn't always manage to practice what he preaches. On one occasion, he tells Harry no one is entirely good or evil. At the same time, he seems wholly convinced that Severus Snape has no redeeming qualities and almost refuses to work with him, even for the benefit of the Order and Harry.
Another of Sirius' pieces of wisdom was if you want to know what a man is like then "look at how he treats his inferiors, not his equals." And at the same time he treats the Black family house elf, Kreacher, with contempt and disgust. This disposition actually directly puts Harry in danger. When Harry gets the vision of Sirius being tortured, he first uses Floo powder to check in at Grimmauld Place. Kreacher, who despises Sirius for his mistreatment, lies to Harry, which sends him into the waiting ambush.
Great: Reassured Him At The End
Still, for all Sirius' faults and instabilities, he wanted what was best for Harry. He wanted him to be safe and happy. Even after his death, he showed up in support of Harry when he used the Resurrection Stone at the end of Deathly Hallows. Harry needs the strength to face Voldemort—and his own death—head on. When Harry asked whether dying hurt, Sirius reassured him. "Not at all," he said. "Quicker and easier than falling asleep." And with his godfather at his side, Harry was ready to face his end.