The death penalty is most definitely on the decline. You can tell by looking at how many places institute it. I think the area that have it are starting to realize that society looks negatively upon it. Killing a criminal doesn't change the crime they committed and does not right any wrongs.
While Texas is still executing people faster and faster every year the state and federal governments are overall slowing down. It had not proven to be an effective deterent and the costs of endless appeals was making life imprisonment more cost effective. It is also a permanent punishment leaving no corrective action for wrongly convicted individuals.
It seems these days that the death penalty is on decline, as it should be. More and more states are getting rid of it all together, and other states that have not gotten rid of it are using it only for heinous crimes. One of the reasons why is that many people have been wrongfully committed for crimes that they did not actually commit.
In the past decade, 5 states have abolished the death penalty. In the remaining states there are constantly protests and attempts at policy to get rid of the penalty. This is probably due to the idea that if an innocent person is put to death, there is no way to take that back. The high number of innocent people in jail is worrying to those who oppose the death penalty.