Amazingly enough, Dr. Smith has had some of these in the series. A good example is near the ending of "All That Glitters" when he becomes genuinely horrified and heartbroken after his newly acquired Midas' touch causes Penny to turn into platinum. He even pleads to the gods asking to them to punish him instead of her. After this, she's brought back to normal. For those who know Dr. Smith, it's hard not to be moved by this demonstration that yes, he does have a heart.
In "The Space Primevals", Don and Dr. Smith are trapped in a cave running short of oxygen and with no hope of rescuing. After years of despising each other, they make amends and admit they consider each other as friends. This is also the only time in the series in which they refer to each other by their first names. Of course, the whole thing is mixed with Funny Moments due to them still Volleying Insults while making peace and Smith insisting that Don calls him Zachary rather than Zach, but none of this diminishes the scene's heartwarming qualities. If anything, it enhances it.
Depending on the Writer, Dr. Smith and the Robot may be portrayed as genuine Vitriolic Best Buds and even be reduced to tears at the thought of never seeing each other again, such as in "Rocket to Earth". Conversely, other episodes show the Robot seemingly going away forever and Smith not giving a dang.
The ending of "The Astral Traveler", where Hamish and Angus are finally freed from their ghostly torment and move on to the afterlife.
1998 Film Version
Will convincing the Robot to fight Smiths programing and help him and the others.
Heck, all the Will and Robot scenes are adorable really.
Robot: Robot will save Will Robinson, Robot will save his friend.
Using the the ship's weapons as a signal flare, so West and the others could find their way back, awww.
Penny trying to console Will over their father not paying attention to them shows that despite her joking threats, she actually does care about her little brother.
John saving Future!Will from falling to his death.
Future!Will: You could have taken the core and left before it was too late?
John: I couldn't let you fall, you're my boy.
Future!Will forcing John into the time portal in order to save the others. Then his jubilation at the fact that the device actually worked.
Future!Will: It worked!
John: Come with us!
Future!Will: ...I can't, only enough power for 'one person, one trip' remember? Take care of 'em, Will...
Will saying goodbye to Dr. Smith in "The Space Croppers". After all the crap Smith's done, Will still wants to be friends with him.
Even better, the look on Dr. Smith's face after Will walks away shows he's really going to miss Will.
Similarly, when Will asks Dr. Smith to be his Parental Substitute when it seems they're stuck on Earth together in "The Raft".