The first meeting between Pocahontas and John at the waterfall. There was no dialogue, but it wasn't necessary to set the mood.
The scene where she visits John Smith as he's imprisoned. "No matter what happens, I'll always be with you... forever." Cue heart-dissolving and lip-quivering from the sheer sweetness of that scene. It's even better accompanied by the deleted song.
Not to mention when they share their first kiss.
Meeko comforting Percy, when he's visibly traumatized by Kocoum's death, and setting aside their differences.
At the very beginning of the movie when a lot the male villagers are returning, the women and children are running to welcome them back. In fact, one of the women runs to a man and tackle hugs him so hard, they both fall back into the river. The chief smiled when he saw that for a reason.
Everyone calming down, with the Tribal leader taking his charge and releasing John Smith from his binds, which causes the two sides to forget about the battle...before Ratcliffe decides to try and bring it back up.
The whole of John and Thomas's relationship counts. They didn't even know each other at the beginning of the movie and by the time the storm threatens to sink their ship John already has a bit of a Big Brother Instinct toward Thomas. Fast forward to the new world and they act as if they've been this way for years.
The brief little hug that Wiggins gives Percy when Ratcliffe and Wiggins are discussing what they'll find in the New World. Really, Wiggins is probably the only character who treats Percy kindly.
Towards the end when Thomas explains to Pocahontas why John has to go back, she puts a hand comfortingly on his shoulder. It shows that she forgives him for his Accidental Murder of Kocoum. The sequel would have shown that Thomas and Pocahontas became somewhat friendly, though his scene was cut.