My favorite is in RE5, after they pull the device off Jill and free her, only to have her tell Chris to leave her behind and go stop Wesker. Chris is a wreck—the graphics had advanced to the point where his feelings were quite clear without him saying much—and Jill tells Sheva, "Take care of him."
Scenes like this are why Resident Evil is respected for its depiction of its female characters.
While that Chris/Jill/Sheva scene was awesome, they all looked like models in that scene.
I personally liked most of the cutscenes in RE5. I particularly liked when Chris goes "Jill, it's me Chris." You can see the desperation/shock in his eyes and voice.
But many of RE6's are quite good too. The cabin scene with Sherry/Jake was memorable. I liked most of the Chris one's but the ones that stood out were Ada's trap, Conflict, and the last few with Chris/Piers.
Steve's death and Ada's death in RE2 were pretty cool too.