After the pilot episode I was willing to watch another episode, but I was still a little on the fence about it.
But when Alara realised she was in command, and the Captain and First Officer were gone, she didn't take it in her stride, and she didn't just go "okay".
spoiler
She went and got a shot of whiskey, and then threw up.
It was at that point I realised that this was how Star Trek would be if the crew were real people, and not Action Figures.
And it was at the point I knew I wanted to watch the rest of the first series because it was going to be good :)