Statistically, clubs scored more points on average last year by going for two. But in my mind, that's just the beginning--and Brees alluded to this as well (click on the link above)--I want teams to also stop punting. If I were an NFL coach, I'd go for it on every single fourth down (I'm certain I've written this before somewhere, but I can't seem to find it).
Unlike the conversion numbers above, it's much more difficult to collect relevant data on this, but I feel as though a team that never punted would score more points by extending drives than it would give up by turning the ball over. I know there's no way this is going to happen in the NFL any time soon, but I'd like to see a major college program commit to it for a full season (maybe a lesser-known school could do it as a publicity stunt, it'd probably help recruit star players on offense as well) and see what happens.
Or even better, the NFL should just eliminate kickers altogether.