Although deterrence is much more than a simple look at only execution rates and murder rates, we do find that, in the US, as executions have risen dramatically, the murder rate has plunged.

From 1966-1980, a period which included the US's last national moratorium on executions (June 1967- January 1976), murders in the United States more than doubled from 11,040 to 23,040. The murder rate also nearly doubled, from 5.6 to 10.2/100,000.  During that 1966-1980 period, the US averaged 1 execution every 3 years, with a maximum of two executions per year.  From 1995-2000 executions averaged 71 per year, a 21,000% increase over the 1966-1980 period.  The US murder rate dropped from a high of 10.2/100,000 in 1980 to 5.5/100,000 in 2000 -- a 46% reduction. The US murder rate is now at its lowest level since 1966 (17).

The Texas example -- The murder rate in Harris County (Houston), Texas has fallen 73% since executions resumed in 1982, through 2000, from 31/100,000 to 8.5/100,000 (18).  Harris County is, by far, the most active death penalty sentencing and execution jurisdiction in the US.  The Harris County murder rate dropped nearly 70% more than did the national murder rate, during similar periods. Texas' murder rate dropped 62% during that same period, or 41% more than the national average.

And "(t)he biggest decline in murder rates has occurred in states that aggressively use capital punishment." (19)

17) i) Homicide trends in the U.S., Long term trends, Homicide victimization, 1950-99, Bureau of Justice Statistics,  Source: FBI, Uniform Crime Reports, 1950-2000
at http://www.ojp.usdoj.gov/bjs/homicide/tables/totalstab.htm, Page last revised on January 4, 2001
(ii) Crime in the United States --  2000, Section II --  Crime Index Offenses Reported, "Murder and non negligent homicide", FBI, Uniform Crime Reports at http://www.fbi.gov/ucr/cius_00/00crime2_3.pdf
(iii) "Number of persons executed in the United States, 1930-2001", Key Facts at a Glance, Executions
Bureau of Justice Statistics, Source: Capital Punishment 2000, December 2001 at
http://www.ojp.usdoj.gov/bjs/glance/tables/exetab.htm
18) Texas Department of Public Safety, Uniform Crime Reporting, Harris County data, from 1982 and 2000 database.
19)  Boston Globe, 10/28/97, p A12

Dudley Sharp - Apart from the fact that your 'evidence' is cited from organisations wishing to justify their decisions and actions....

How many people put to death by US law were innocent of committing murder. I would be interested in those statistics please.

As of  1/1/03, The National Coalition to Abolish the Death Penalty (NCADP) claims that "Twenty three (23) innocent people have been mistakenly executed (in the US) this (the 20th) century." (32) This is a common false claim, even though the authors of that 1987 study, in response to a deconstruction of their work, stated, in 1988, that "We agree with our critics that we have not proved these (23) executed defendants to be innocent; we never claimed that we had." (33).  The NCADP is well aware of this, yet it doesn't stop their deception.

Barry Scheck, cofounder of the Innocence Project and featured speaker at the National Conference on Wrongful Convictions and the Death Penalty (11/13-15/98), stated that he had no proof of an innocent executed (in the US since 1976) (34).

Not even the nation's leading, biased source for anti death penalty information, the DPIC, says there is proof of an innocent executed. They list 5 "doubt" cases (35): Gary Graham, Joseph O'Dell, Roger Keith Coleman, Leo Jones and David Spence.  A review shows how deceptive the DPIC case descriptions are (36) and how lacking any proof of innocence is.

The Texas case of Lionel Herrera, like others, nationally, has been labeled, by many death penalty opponents, as an innocent executed. A comment from Supreme Court Justice O'Connor. "[T]he proper disposition of this case is neither difficult nor troubling . . .  The record overwhelmingly demonstrates that petitioner [Herrera] deliberately shot and killed Officers Rucker and Carrisalez the night of September 29, 1981; petitioner's new evidence is bereft of credibility.  Indeed, despite its stinging criticism of the Court's decision, not even the dissent expresses a belief that petitioner might possibly be actually innocent." Herrera v. Collins, 506 US 390, 421(1993) (O'Connor, J., concurring)

Of all the world's social and governmental institutions, that do put innocents at risk, I am aware of only one, the US death penalty, that has no proof of an innocent killed since 1900. Can you name another?

Depends how you define innocent, DS. But just off the top of my head, how about Ricky Ray Rector, so profoundly brain-damaged he was incapable of understanding he was about to be killed, and put some of his last meal away "for later". The death penalty did not deter him from the original crime, and he posed no further risk to society. And while we're looking at statistics on deterrence, Stephen Levitt makes a very convincing argument that Roe v Wade was a far more important contributing factor to the fall in the crime rate overall and the murder rate in particular. And no doubt, with sufficient ingenuity and incentive, someone could convincingly show the fall could be attributed to sunspot activity. Can we please deal less with statistics (dubious or otherwise) and more with the question of what happens if someone is executed despite their being innocent. But to add one thing to your stats, some of the technicalities you dismiss are such things as "inadequate assistance of counsel", one case featuring a defence lawyer who was asleep through much of the trial. A high price to pay for someone else's bit of a kip.

"Death penalty
Latest news and actions
The death penalty is the ultimate cruel, inhumane and degrading punishment.
It violates the right to life.
It is irrevocable and can be inflicted on the innocent. It has never been shown to deter crime more effectively than other punishments."

"6. The deterrence argument
Scientific studies have consistently failed to find convincing evidence that the death penalty deters crime more effectively than other punishments. The most recent survey of research findings on the relation between the death penalty and homicide rates, conducted for the United Nations in 1988 and updated in 2002, concluded: ". . .it is not prudent to accept the hypothesis that capital punishment deters murder to a marginally greater extent than does the threat and application of the supposedly lesser punishment of life imprisonment.”
(Reference: Roger Hood, The Death Penalty: A World-wide Perspective, Oxford, Clarendon Press, third edition, 2002, p. 230)"

"10. The death penalty in the USA
• 65 prisoners were executed in the USA in 2003, bringing the year-end total to 885 executed since the use of the death penalty was resumed in 1977. The 900th execution was carried out on 3 March 2004.
• Over 3,500 prisoners were under sentence of death as of 1 January 2004.
• 38 of the 50 US states provide for the death penalty in law. The death penalty is also provided under US federal military and civilian law."

Source:

http://www.amnesty.org.au/whats_happening/death_penalty/facts_and_figures?MySourceSession=6fa70073f526d8611a630c5b981c0eae

Dudley Sharp
How does the death penalty aid the progression of a civilised nation?

Statistics aren't as unreliable as many people say, it's just that its very easy for people to omit important parts or manipulate in order to further their ideology. It can be countered easily though:

"From 1966-1980, a period which included the US's last national moratorium on executions (June 1967- January 1976), murders in the United States more than doubled from 11,040 to 23,040."
Which according to your first cite was merely the continuation of a pre-existing trend.

"The murder rate also nearly doubled, from 5.6 to 10.2/100,000."
I'd hope so.

"From 1995-2000 executions averaged 71 per year, a 21,000% increase over the 1966-1980 period."
Because it was considered illegal during those years.

"The US murder rate dropped from a high of 10.2/100,000 in 1980 to 5.5/100,000 in 2000 -- a 46% reduction."
And it dropped from 9.8/100,000 in 1991 to 5.5/100,000 in 2000 -- a 44% reduction.
Ie. for the 15 years after the death penalty was restored there had only been a 0.4% drop in homicide rates.

"The US murder rate is now at its lowest level since 1966"
As Anomie said, perhaps due to abortion. (Freakonomics)

"The Texas example -- The murder rate in Harris County (Houston), Texas has fallen 73% since executions resumed in 1982, through 2000, from 31/100,000 to 8.5/100,000"
Even at it's lowest level Harris County has a rate 50% higher than the US average of 5.6 per 100000; it seems to be a statistical outlier. Given the higher murder rates on average in Texas, it is to be expected that any social changes affecting murder rates will have the greatest effect there.

Here's some more stats, as printed in the New York Times, September 22, 2000.
"Indeed, 10 of the 12 states without capital punishment have homicide rates below the national average, FBI data shows, while half the states with the death penalty have homicide rates above the national average. A state-by-state analysis found that during the last 20 years, the homicide rate in states with the death penalty has been 48 percent to 101 percent higher than in states without the death penalty."