Interesting question. Many people, whether or not they are Christians, support the death penalty because of concerns that brutal criminals will be released into their communities and because they haven't yet looked at the death penalty system in action. For example, some of the answers you have received are mistaken on the facts.
129 people on death rows have been released with proof that they were wrongfully convicted. DNA, available in less than 10% of all homicides, can’t guarantee we won’t execute innocent people. No system crafted by human beings gets it right every time. Human beings are fallible.
The death penalty doesn't prevent others from committing murder. Homicide rates are higher in states and regions that have it than in those that don’t.
Life without parole, on the books in 48 states, also prevents reoffending. It means what it says, and spending 23 of 24 hours a day locked in a tiny cell is not a picnic. Life without parole costs less than the death penalty.
The death penalty is much more expensive than life in prison, mostly because of the upfront costs of legal process which is supposed to prevent executions of innocent people. (upfront=before and during the initial trial)
The death penalty isn't reserved for the worst crimes, but for defendants with the worst lawyers. It doesn't apply to people with money. When is the last time a wealthy person was on death row, let alone executed?
The death penalty doesn't necessarily help families of murder victims. Murder victim family members have testified that the drawn-out death penalty process is painful for them and that life without parole is an appropriate alternative.
Problems with speeding up the process. Over 50 of the innocent people released from death row had already served over a decade. Speed up the process and we will execute innocent people.
Sources:
Death Penalty Information Center, www.deathpenaltyinfo.org, for stats on executions, reports on costs, deterrence studies, links to FBI crime stats and links to testimony (at state legislatures) of victims' family members.
FBI http://www.fbi.gov/ucr/cius2006/data/table_04.html
The Innocence Project, www.innocenceproject.org
http://www.deathpenaltyinfo.org/COcosttestimony.pdf page 3 and 4 on why the death penalty is so expensive
http://www.njadp.org/forms/signon-survivor.html for statements of victims’ families
http://www.usccb.org/sdwp/national/deathpenalty/ for the Catholic Bishops Campaign to abolish the death penalty