Since his debut in Sonic Adventure 2, Shadow's garnered quite a reputation both in and outside the Sonic the Hedgehog fanbase. He originally opposed Team Sonic with Dr. Eggman and another new character at the time, Rouge the Bat. Over time, he fell into the role of an anti-hero, not a textbook villain, but not exactly a kind-hearted hero either. Despite some of his actions, Shadow's saved the day alongside Sonic on more than one occasion.
Recent entries in the Sonic the Hedgehog franchise seemed to embrace Shadow's more "edgy" and "loner" side, but he still has his good moments. However, Shadow's more memorable deeds were present in the 2000s era of Sonic games. During this period, Shadow was commonly featured as a playable character, and he even managed to get his own game - Shadow the Hedgehog. Whether Shadow will have more heroic deeds to come is up to the writers.
7 Sonic Rivals: Stopping Eggman Nega
Sonic Rivals and its sequel Sonic Rivals 2 were one of the few Sonic games to not release in Japan. In these, gamers chose between four different characters (eight in SR2) with Shadow being one of them. Shadow learns that the Eggman he's been chasing throughout the game is actually Eggman Nega, who arrived from the future along with Silver. Nega has this odd camera that allows him to turn people and objects into cards. By the climax of Shadow's story, Eggman Nega decides to turn Shadow's world into a card by using Rouge's card as fuel. With some help from Silver, Shadow puts a stop to Nega's plans and restores Rouge to normal while Nega gets turned into a card himself.
Compared to his other heroic acts, this is quite tame, and Shadow even decides not to help Rouge look for the remaining cards after he's rescued her. However, it's worth mentioning that Shadow will go out of his way to get rid of anything that threatens his world.
6 Sonic X: Fighting the Metarex
Sonic X was the anime spinoff of the Sonic games, introducing anime-exclusive characters such as Chris Thorndyke and Cosmo. Shadow appeared in the second season, which largely followed the Sonic Adventure and Sonic Adventure 2 storylines with some minor changes to accommodate the anime characters and storytelling.
By season 3, Shadow's working with Rouge alongside Dr. Eggman. However, he realizes the bigger enemy is the Metarex and eventually joins forces with Sonic's team after clashing with them several times over the course of the season. Shadow's biggest moments in Sonic X are in episode 68 and episode 77-78. In episode 68, Shadow helps a pilot named Molly fight back against the Metarex who have invaded her planet. Molly eventually sacrifices herself during the fight (runs away in the 4kids version), which pushes Shadow to destroy the fleet of Metarex. He then builds a grave in her honor. Episode 77 and 78 have him work with Sonic in their Super Forms to destroy Final Mova, with episode 78 resulting in him sacrificing himself much like Molly had. Super Shadow uses Chaos Control right before Dark Oak's Planet Egg explodes, warping himself and the Planet Egg away from his allies. Despite this, it's implied Shadow survived in the Japanese ending, where his silhouette can be seen over Molly's grave.
5 Sonic 06: Trying To Stop Mephiles
Sonic the Hedgehog 2006 marks one of the few games where Shadow truly played the role as a hero. In this game, he works for GUN and opposes Eggman, a stark contrast to Sonic Adventure 2 and Shadow the Hedgehog. This version of Shadow is consistent with his backstory, featuring a Shadow more sure of himself and working alongside Rouge and Omega to protect the Scepter of Darkness from Eggman. Shadow's main conflict this time is against Mephiles the Dark. It's one of the few times when Shadow fights for good instead of his own reasons.
During his story, Shadow learns from Mephiles that humanity will once again turn on him and keep him locked up for centuries. Despite this, Shadow refuses to side with him, claiming he "determines his own destiny." The remainder of Shadow's story is spent trying to seal Mephiles in the Scepter of Darkness. By the final episode, Shadow, alongside Sonic and Silver, defeat Solaris.
4 SA2: Saving Rouge From Prison Island
In Sonic Adventure 2, Rouge goes to Security Hall to steal three Chaos Emeralds needed for the Eclipse Cannon aboard the ARK. Eggman and Shadow plant bombs all around Prison Island, setting the timer to explode after 10 minutes. Unfortunately, Rouge gets captured and locked up in the vault. At first reluctant, Shadow turns around and warps into Security Hall to rescue her.
Shadow's reasoning for saving her was to secure the Chaos Emeralds, but Rouge still thanks him regardless, mentioning how she hadn't expected Shadow to save her. This isn't the only time Shadow's saved Rouge: he's pushed her out of Omega's line of fire in Sonic Heroes and even caught her when she was struck down by Eggman in Sonic the Hedgehog (2006). Whether Shadow admits it or not, saving Rouge was a heroic act.
3 Sonic 06: Saving Sonic From Silver
Another Sonic 06 example in which Shadow stops Silver from killing Sonic midway through the game. Shadow and Sonic have been known to be at opposite ends on more than one occasion, but this is one of the few times when he's shown saving the blue blur from danger. It should be noted that Silver very well could have killed Sonic had Shadow not intervened. Before Sonic leaves, he gives Shadow a thumbs-up in thanks before rushing off to rescue Elise from Eggman. This scene alone shows how far Sonic and Shadow's relationship has come since their days in Sonic Adventure 2.
2 Shadow the Hedgehog: Destroying the Black Arms
In Shadow the Hedgehog, players need to unlock all endings to get the true/canon ending. This technically means that any of Shadow's endings that follow the "Hero Missions" are heroic, but they're not canon, so they don't exactly count.
The true ending has Shadow getting all the Chaos Emeralds and learning the truth about his past from a recording left by Gerald Robotnik and Maria. This gives Shadow the push he needs to finally fight back against Black Doom, who's been manipulating him the entire game. By the end, Super Shadow defeats Devil Doom and warps the Black Comet into space. With the Eclipse Cannon, he destroys the Black Comet and the Black Arms, saving humanity. Finally, Shadow's story closes with him leaving the ARK for good, accepting himself for who he is and leaving the past behind him.
1 SA2: Shadow's Sacrifice
While it's clear that Shadow's still alive in Sonic canon, the ending of Sonic Adventure 2 originally ended with his sacrifice. Thanks to Amy Rose, Shadow remembers his real promise to Maria, and he rushes off to help Sonic and the gang stop the ARK from crashing into earth. He defeats the Biolizard by himself, but when the Biolizard attaches himself to the ARK, he ends up working with Sonic to defeat the Final Hazard.
Unfortunately, in defeating Final Hazard, Super Shadow burns through all his energy and ends up falling to Earth. Sonic even refers to Shadow as a "brave and heroic hedgehog" following his sacrifice. In sacrificing himself, Shadow believes he's fulfilled his promise to Maria.