In Chapter 6: Bejewled. In order to calm a panicking Naru down, Usagi reveals that it's her under Celestial Warrior Moon's mask and then promises to always protect her best friend. D'aww.
Ami gets a decent one in Chapter 2. Despite being a shy, petite, and skinny little thing, she actually tries to give The freaking Rake a Tap on the Head with a wooden chair in order to save Usagi. It doesn't work, but the fact that she even had the figurative balls to stand up to that eyeless monstrosity for someone she barely knew at that point still warms the feels.
Also from Chapter 2, the poor exterminator who saved Naru's mother from The Rake. He didn't have to haul her up the stairs to safety. He could have just left her to save his skin, but no, after The Rake attacked him, his partner, and Naru's mother in the basement of the latter's home, he managed to get away long enough to get her safely up the stairs to the Usagi and company. It makes his fate in getting dragged back down the steps to be viciously murdered and devoured all the sadder.
Off-screen, but Makoto apparently tried to convince Ami's mother that her daughter's schedule wasn't healthy, and was wearing Ami down too much.
The occasions where Rei shows genuine concern and affection for Usagi, in spite of all the blonde's faults and mistakes.
An odd one, but Zoicite and Kunzite have a touching moment after the former is bed-ridden after too close a call with Mars. They're evil, but they are very clearly in love.
Also, Nephrite's feeling for his dead lady still bother him 1,000 years later, causing problems when he has to crash another woman's wedding and kill her. Then we get another CMOH when Jadeite instantly covers for Nephrite to Beryl.
In chapter 37 it's rather sweet that the Reverend is willing to take the time to talk to a troubled foreign girl he's never met before (Usagi). Then we have the heartwarming conversation where she pours out all her fears and flaws that the Keepers have been niggling her about, showing how insecure she really is, and he consoles her that she's not alone. Then when she reveals that she's a Warrior and that the monsters are coming, he trusts her and goes with her and the others.