I die everytime I read this part:
"Edward! You stayed!" I rejoiced, and thoughtlessly threw myself across the room and into his lap. In the instant that my thoughts caught up with my actions, I froze, shocked by my own uncontrolled enthusiasm. I stared up at him, afraid that I had crossed the wrong line.
But he laughed."
--Twilight, page 312-313
It shows that he really, truely accepted Bella into his life. This scene is cutesy and playful on the surface, but if you look into it, it means so much more.
Ahh, one of my favorites of all time, I would probably put this at the top of my list. There is just something so sweet and tender and vulnerable between Bella and Edward the morning after the meadow in the first book.
I don’t know if this counts specifically as romantic
, but there is also that incredible reunion in New Moon and the plane trip back home. Bella refusing to sleep, desperately suppressing any hope that Edward still loves her, but both being unable to keep their eyes off of each other.