Kara v Vartox, Kara pushing Vartox's axe back toward him proving she is the stronger, just before the axe explodes.

5. Kara hugging Alex and holding J'onn's hand, forgiving them for their complicity/perceived complicity in her Aunt Astra's death (Solitude)

4. Every instance of Kara vs. Bizarro (Bizarro)

3. Alex saving Kara from the Black Mercy (For the Girl Who Has Everything)

2. Cat pronouncing Kara's name right and promoting her (Better Angels)

1. Kara stopping a robbery without her powers/Hank revealing his true identity to Alex (Human for a Day)

Cat accusing Kara of being Supergirl at the end of "Hostile Takeover"
Cat & Kara's balcony scene in "Myriad"
Red-K Kara going off on Alex
a couple of others that have already been mentioned

I have to split mine up....

Action scenes

1. Kara destroys Red Tornado "Red Faced"
2. Disarming the nuclear missile "Solitude"
3. Flying Ft. Rozz into space "Better Angels"
4. Fight between Astra and Kara ep. "Hostile Takeover"
5. Fight between Non and Kara ep. "For The Girl Who Has Everything"

Dramatic scenes

1. Kara pleading forgiveness from Alex "Falling"
2. Kara forgives Alex for killing Astra "Solitude"
3. Kara lashes out at the AI of her mother "Hostile Takeover"
4. Alex talks Kara back from the Black Mercy "For The Girl Who Has Everything"
5. Winn and Kara in her apartment the "um, no kiss" moment. "Child's Play"

Funny scenes

1. Barry brings the Ice Cream "Worlds Finest"
2. After Kara's airplane save in her apartment "Pilot"
3. Fluffy "Stronger Together"
4. I can keep a secret "Blood Bonds"
5. Where's my cape "Pilot"

1.) Falling: Kara talking to Alex, realizing what she had done.

2.) How can you NOT love Kara lifting Fort Rozz--epic Blake Neeley music to enhance it, even.

3.) Kara and Alex's 1st couch scene..."Right in the face!"

4.) Kara saves the plane (it's what made me realize, I was HOOKED)

5.) Deleted Scene...Alex and Kara in ALEX'S appartment

Honorable Mention: Barry brings icecream