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:
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:
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):
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:
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 in some cases to follow the law of Moses?.
The bible teaches the sanctity of life. If we are to upheld this concept then the following are unacceptable:
The pre-born are protected in Old Testament Law. (see Exodus 21:22-25)
Permitting the murder of innocents pollutes the land. (see Numbers 35:33-34)
Believers are charged with defending life. (see Proverbs 24:11-12)
God hates those that shed innocent blood. (see Proverbs 6:16-17)