This solution is applied, expressly or tacitly all over the world. The usual alternative for extremely serious crimes remain life imprisonment. However, "although nearly all member states [of the EU] provide for this type of punishment in their respective penal codes either as a possibility or mandatory, it is understood rather as a principle than as common knowledge" (Use of the Death Penalty Worldwide)

What would it take to work?

There is a big a step ahead that needs to be taken in order to abolish the death penalty, and it involves the mentality of the people. Many Americans are avid for larger and more powerful guns. How would such people accept that the dead penalty is inhumane? Perhaps social campaigns could prove useful in such a case.

What is the history of the death penalty in the U.S.

The United States have a long history of applying the death sentence. Its violent past was perfect for the development of such practices. What is truly disturbing is that mentalities do not seem to change. Southern states still apply predominantly the death penalty, as numerous articles and statistics prove. "America's high ranking among the most frequent deployers of capital punishment is due in surprisingly large part to the predilection of one region -- and particularly one state, and even more particularly one county -- for the practice. ... Fifteen southern states have...

executions since 1977. Texas alone, with 289 executions, is responsible for 35% of the total during that time, and has often ranked among the top ten countries in the number of people it executes each year. And Harris County, which encompasses Houston, has executed more people than all states except Texas and Virginia over the past quarter century." (Moral Justice)
The evolution of death the death penalty in the U.S. (source: Moral Justice)

Reference:

1. Joynt, Jen, Shuchart, Carrie "Moral Justice," Atlantic Monthly, 10727825, Mar2003, Vol. 291, Issue 2 ("Moral Justice")

2. Dority, Barbara "Not In My Name," Humanist, 00187399, Mar/Apr93, Vol. 53, Issue 2 ("Not in My Name")

3. "Death Penalty Vigil" Christian Science Monitor, 08827729, 11/17/99, Vol. 91, Issue 246 ("Death Penalty Vigll")

4. "Use of the Death Penalty Worldwide," International Debates; Feb2004, Vol. 2 Issue 2, p34, ("Use of the Death Penalty Worldwide")

5. Buckley Jr., William F, "The Fight to Kill," National Review, 00280038, 10/27/2003, Vol. 55, Issue 20 ("The Fight to Kill")

6. Van den Haag, Ernest, "The Ultimate Penalty...," National Review, 00280038, 06/11/2001, Vol. 53, Issue 11 ("The Ultimate Penalty")

7. Robinson, Mary Frances "A Humane Death Sentence?." Humanist, Jul/Aug2000, Vol. 60 Issue 4, p5,

8. Hartnett, Stephen "The Death Penalty: An American History" (Book), Journal of American History, Dec2003, Vol. 90 Issue 3, p983,

9. Janis, Lauren "At The Execution," Columbia Journalism Review, Jul/Aug2001, Vol. 40 Issue 2, p8

10. Sotirovic, Mira "Effects…