Penguin may have been one of the many (many) villains at the center of Gotham, but that doesn't mean that he was always the bad guy... or at least, that he only ever did terrible things. Sure, he was a snitch, a traitor, utterly self-serving, often considered insane, and a cold-blooded killer, but he also spent a surprising amount of his time on the show trying to do the right thing - or at the very least, accidentally doing the right thing while trying to take care of himself.
From errand boy to Fish Mooney through time as Mayor of Gotham, inmate at Arkham, and leader of his own gangs, Penguin had his good moments - and these are some of his best.
Saved The Mayor (& Worked With The Police)
From the start of Gotham, Penguin has been all about selling information to whoever is going to help him out - and while most of the time, that's a terrible way to behave, he's actually helped the police in some pretty impressive ways over the years. As an informant, Penguin allowed the GCPD to stay on top of some of the criminal activity in the city... and his information actually saved the life of the then-mayor Aubrey James. It was right at the start of his long and complex relationship with Jim Gordon, but no matter what, he did save a life.
He's A Loving Son
For all his faults, Penguin is consistently caring, loving, and protective of one person that he would never betray - his Mommy. Gertrude is the center of his life, even if she doesn't quite know what her son is up to most of the time, and while he lies to her, he does it to protect her. He will murder anyone who so much as insults his dear mother, and when she was being held captive, he even (sincerely) offered up his own life in exchange for hers.
Got Jim His Job Back
Jim Gordon's history with the GCPD in Gotham isn't an easy one - from his early days as the only cop on the force willing to stick to the rules, he's been at odds with much of the GCPD. He's lost his job with them in the past, and has even been on the run from them! However, when he lost his job, it was Penguin who got Commissioner Loeb to resign and reinstate Jim. Admittedly, this was all part of their favor-for-favor relationship, but it's still something good he did for someone he almost considered a real friend.
Saves Jim's Life (And Gives Him Sanctuary)
Onto more good deeds that Penguin did for Jim over the years - not only did he get him his job back, he actually saved his life. When Jim was about to be brutally murdered by crooked cops (at the behest of Theo Galavan), Penguin swooped in and saved him.
Then, he brought Jim to Nygma's home (where he was staying), and gave him sanctuary while he was on the run. He didn't have to do any of it, but Penguin has always had a soft spot for ol' Jim.
Just Wanted To Be A Part Of His Father's Life
Once again, one of the most lovable moments in Penguin's story is when he is attempting to connect with a parent. After his mother is killed, Penguin gets a second chance when he meets his long-lost father. Admittedly, Penguin is operating under some heavy duty anti-crazy conditioning at the time, but he still wants to be honest, and do whatever he can to be a son to the man he never knew. It's a sweet moment for Oswald... until, of course, his father's family murders him, causing Penguin to flip back to his bad side, slaughter them, and serve them up for dinner.
Saves Gotham From Theo Galavan
Gotham has dealt with more than its fair share of evil villains over the years - and Theo Galavan/Azreal was definitely one of the biggest (especially for Bruce Wayne and Jim Gordon). However, Penguin was on the side of good for this fight. He teamed up with people to try and deal with Theo, and actually managed to kill him twice! First, with the help of Jim Gordon and an umbrella down the throat, and then (having learned his lesson) with a rocket launcher.
Actually Tries To Be A Good Mayor
Penguin is always after power, and actually gets it a few times in Gotham - and once, even gets it (almost) legitimately. As Mayor, Penguin might not always be the most upstanding citizen, but he does actually try.
He's also on the side of 'good', as far as Gotham goes; he wants the city to be peaceful and prosperous. Admittedly, he only wants that because then he would get the credit for it (and he would keep the power he loves), but he still wants it.
Created The Pax Penguina
Penguin might want power, but he actually recognizes (for a while) that the best way to get it and hold it might be to have both the criminal and the public's support. Hence: the Pax Penguina. This system actually legitimized crime... but only for very specific criminals who got licenses from Penguin. It actually worked (kinda) too - crime rates in Gotham were impressively low, and people could actually feel safe (or safer, anyway!). Of course, the Pax Penguina didn't last, but none of Penguin's schemes ever do.
Saved Little Orphan Martin
It's rare for Penguin to really care about anyone else - he loved his mother, of course, and Nygma, but other than that, true friends are rare for Cobblepot. However, we did get a look at his softer side when he became close to little orphan Martin. Penguin first met the boy when he was being bullied, and clearly saw something of himself in the boy, because he took him under his wing. He even managed to fake Martin's death and spirit him out of Gotham to try and save him, because he cared about the kid so much.
Stood Up For Gotham In The Final Fight
While there are plenty of smaller times where Penguin has actually done some good, this list wouldn't be complete without the most obvious one - standing up against Bane's army at the end of the show. Gotham would have totally fallen (further than it did when it became No Man's Land) if not for the people who stood up and gave their all to fight for it - and Penguin was one of those. He even sacrificed an eye - giving him his trademark monocle. Say what you will about the criminal, Penguin is always there for Gotham in the end.