Yoda teaching the Younglings, and them all helping Obi-Wan, is a purely adorable scene.
Watto seemed genuinely happy to see Anakin again, considering he owned him and Anakin does not return the sentiment.
The Anakin and Padme relationship attracts some bashing, but Padme's Anguished Declaration of Love at the end of the film is actually a bit moving.
Jango Fett may be a ruthless bounty hunter, but you can't deny he's a very doting father to his clone, Boba Fett. Boba clearly adores him in return which makes Jango's death pretty tragic despite him having it coming.
Though this definitely is more of a Tear Jerker than anything else, Shmi Skywalker, after having been tortured by the Tusken Raiders, at the very least, got to see her only son one last time in her final moments.
The secret wedding of Padme and Anakin.
Behind the scenes, Daniel Logan grew up without a father. The first thing Temuera Morrison said to him was that their roles would be easier if they actually referred to each other as "dad" and "son." They've stayed in touch ever since.