Some Christians are for and some are against capital punishment. However what does the Bible have to say about it?
There are a host of references to capital punishment in the Bible - the first of which is in Genesis shortly after the Flood in Genesis 9:6:
Whoever sheds man's blood, by man his blood shall be shed, for in the image of God He made man.
Christ did not condemn the Roman soldiers for executing the thieves who were crucified with Him.
Paul does not deny the government the right to execute him if he has done something worthy of death in Acts 25:11a:
"If, then, I am a wrongdoer and have committed anything worthy of death, I do not refuse to die"
Excluding specific commands regarding what was worthy of death to the nation of Israel under God's special covenant, it would seem that the Bible takes a neutral-to-positive view of the death penalty: the Noahic covenant was made with only 8 people on the planet - the forebears of all of modern humanity. As with Adamic covenants, since the it was made to the federal representative(s) of humanity, it still applies today - especially in light of the end of the covenant (Genesis 9:12ff):
God said, "This is the sign of the covenant which I am making between Me and you and every living creature that is with you, for all successive generations"
In John 7:53-8:11, a crowd of men who are about to stone an adulteress to death, fulfilling the Law of Moses, are stopped when Jesus condemns them by asking for the one without sin to go ahead and cast the first stone.
Additionally, Matt. 7:1-2 states:
Do not judge, or you too will be judged. 2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.
Also taking into account that New Testament teaches that the Law of Moses is no longer binding (Romans 10:4; Galatians 3:23-25; Ephesians 2:15), it seems very clear to me that the Bible opposes death penalty.
Edit 1: H3br3wHamm3r81 makes a good point that many biblical scholars question the authenticity of the Pericope Adulterae (John 7:53-8:11). He gives more details in the answer to the question, Is it a sin or forbidden to follow any of the parts of the Law of Moses?.