Near the beginning of the film, John (the then selfish cynic) going back and trying to save Coronel Powell, Powell even returned the favor not long after when the Thern nearly stabbed John in the back. Shame it ended on a tearjerker.
John defending Woola, the Tharks' guard dog from being beaten by the Tharks' for interrupting their evening meal. He didn't have to do help it, but he did anyway despite the risk.
John stepping up to defend Dejah Thoris from a bunch of Zodangan soldiers, sure she proves she's no Distressed Damsel and can protect herself. But you can tell under her snarky comments that she found his act of chivalry more endearing than irritating.
Woola refusing to leave John's side as the Warhoons approach.
Sola and Woola waiting outside Zodanga all that time John was being kept there.
At Carter and Dejah's wedding, Sola wiping a tear from Tars Tarkas's face. Also qualifies as a funny moment.