Heartwarming / Sherlock Holmes in the 22nd Century
In the second episode when Holmes gets to move back into 221B Baker Street. He promptly asked Watson to move in with him cementing that he cared for the Watson Robot.
Rewinding the episode a couple of minutes... After his poor treatment of Watson in the first half of the episode, Holmes thinks he's lost him and goes into denial. Then Watson reappears, much to Holmes's joy.
When Holmes fakes his death again, Watson is brooding over his loss. When someone enters the room, he thinks initially thinks it's Holmes.
"The Fall and Rise of Sherlock Holmes":
Lestrade: "Do you miss him [Watson]?"
Holmes: "More than I care to admit."
"The Deranged Detective" is one big episode of heartwarming with the way that Holmes deals with Lestrade's apparent insanity.
In the Christmas Episode, Watson has a present for Holmes... which, unfortunately, we never see opened.
In "The Sussex Vampire" there's the concern Holmes has for Robo-Watson in a case dealing with a electronic vampire. The most touching of which is Holmes learning there may be two such vampires, and his immediate thoughts aren't for the case...
Holmes: Watson may be in more danger than I thought.
The Ship Tease between Tennyson and Amanda is adorable as well. Especially since Wiggins and Deidre tend to pick on Tennyson a fairly bit (albeit playfully but still).
"The Five Orange Pips" when a client prejudiced against robots says that he will not permit Watson coming along on a case. Holmes puts his foot down and says that if Watson isn't coming, then neither is he.
The resolution of "The Crooked Man". Victor may or may not be made normal again, but he and Nancy are reunited and still love each other.