Generally speaking, I like it.
It has a bit of a glossy, cheesy vibe that reminds me of the Robin Williams/Sarah Michelle Gellar show The Crazy Ones for some reason.
It also got unnecessarily political in the first 30 seconds, which is annoying.
But I do like how they tackle the use of the word "girl" rather than "woman" for the hero's name.
If I had seen this trailer last year, I would have been less enthused. But two things are influencing my perspective:
1. The Flash Season One. I remember seeing the first teases for the new Flash show and I was very much underwhelmed. I didn't like the suit and I wasn't crazy about Grant Gustin. But having watched it since it premiered, it might be my favorite show on TV right now. Yes, it does have Dawson's Creek-esque angst to it and can be a little corny. But it is still fantastic fun. I think that this new Supergirl, produced by the same people as The Flash and Arrow, could also be as fun.
2. Felicity Smoak. Speaking of Arrow, my favorite character on that wonderful show is Felicity Smoak. She is perfectly adorkable. Kara in the Supergirl trailer looks like Felicity with super powers. And that is a show I would watch.