In Inspector Gadget, the trend isn't so much toward Crowning Moments of Heartwarming as it is little kernels that, when added up by the viewer, lead to Crowning Realizations of Heartwarming (such as the relationship between Gadget and Penny being MUCH closer to father and daughter than uncle and niece, or that Penny, despite how incompetent she KNOWS her uncle is, still trusts him to care for and protect her). There are a few, though.
In the episode "A Star is Lost", there's a record that painfully puts people to sleep. Penny and Rick Rocker are put to sleep by it, then Gadget comes along and falls asleep on top of the record player, stopping the record. When they all wake up, Gadget is in pain not only from the record, but from squishing his face on the player, and still manages a pained but sincere smile upon seeing Penny.
In "The Great Divide", Gadget falls into a mountain river from a great height, and the warden (working for M.A.D.) tells Penny Noone Could Survive That. Penny's heartbreak is clear in her voice — and of course, Gadget survives (his only injury, being a little wet and having some fish in his clothes) and Penny runs up to him and hugs him.
In "Gadget's Roma", Gadget and Gadgetorum's second hug (the one after Gadgetorum says "You do look-a familiar") is incredibly adorable. Gadgetorum's expression changes from one of surprise and confusion (even fear, from the way he flinches away from Gadget when he reaches for him) to mirroring Gadget's affection (as he returns the hug) once he realizes what's happening. And when you think about it, Gadgetorum being a slave that "hasn't been out of the Colosseum in years", it's probably the first real, unconditional affection that he's ever been shown in his adult life — no wonder he's confused!
Gadget pretty much spends the whole of the SNES game in Papa Wolf mode, but the clincher is at the end after you beat Dr Claw. Dr Claw decides to drop Penny out of his Cool Airship hideout, so Gadget jumps after her to her rescue. Seeing Penny embracing Gadget as they safely float down just makes one feel all warm and fuzzy inside, proving that all this time her faith in him has not been misplaced. Bonus points for also being a Crowning Moment of Awesome.