All the officers of the RPD got together to throw new recruit Leon a welcoming party. It got cancelled, but hey, it's the thought that counts.
Given that Sherry is quite the Woobie who tends to hug Claire a lot, she can get a few 'Awww's' out of the player.
Doubly so during gameplay if you have Sherry following you and you stand still. When she catches up to you, if you don't move, she holds Claire's hand until you move again. A very sweet example of passive Video Game Caring Potential.
Leon and Ada having a tender moment in 2 after Birkin injures Ada and Leon fights him off, seen here.
Leon: I told you, it's my job to look after you.
Ada: But, you'll be in danger if you stay with me. I know I've only known you for a short period of time, but I really enjoy being with you.
Ada: I know, I'm not capable of caring about anyone, but, I don't want to lose you.
All the times Ada helps and saves Leon from then on shows she means it.
Towards the end of the "Leon A" scenario, Ada holds Leon at gunpoint demanding that he hand over the G-virus. When Leon refuses, not only does Ada lower the gun, but after she falls, you find out that it wasn't even loaded. So much for being able to care about people, Ada.
One for the novels: Ada attempts to flirt with Leon when she thinks he's starting to work out that she's not who she says she is. She believes he is interested before he steps back and openly says he's scared and just wants to be a good cop. Ada's reaction is her seeing he's not just trying to be macho, and is more of a man for the admission.