I cant choose just one scene. that’s impossible. 
but my fav ones would be:

• 1x03- Elena tells Damon she is sorry about Katherine. that was the very start of everything. that was when, the first time, in 145 years, someone noticed Damon was hurt, and that meant a lot to him, even tho he tried to pretend it didnt. 
• 1x11- drinking and just having fun in Georgia
• 1x19- Miss Mystic Falls Dance 
• 2x08- when he tells her he loves her and makes her forget. I cried watching this scene. it was the most selfless thing anyone could have ever done for someone they love. 
• 2x21- the cemetery scene. even tho they didnt say a word to each other, you can see how much them both mean to each other. Elena was trying to be strong, trying to hold her tears, but when they looked at each other, she knew she didnt have to do that anymore, that she didnt have to pretend with him. and his little smile basically said “it’s gonna be ok. I’m here for you”, and she, somehow, ‘listened’ to it, and just cry. 
• 2x22- the deathbed scene. not just because they kissed, but because of all the beautiful and meanful things they said to each other
• 3x05- Damon carrying her out of the hospital, and also when she asks where he was almost crying. that shows how much she needs him. 
• 3x10- the kiss scene. but also not just because of the kiss. but because of everything they said (especially Elena).