I am supportive of the death penalty in the case of serious crime because if they're dead they're not a burden to society eating up taxpayer money doing nothing etc. etc. EXCEPT sometimes death is too easy a punishment for some crimes, and the people that committed them should be locked up for life to suffer instead.
Having said that, I do recognise the fact that sometimes innocent people are convicted (horrible, I know) so I would only implement the death penalty in cases where the person is without a doubt guilty, and even so after a period of time. I'd also take into consideration if that person has children, sick parents or some other reason why their being alive in prison is necessary/beneficial.
I'm also supportive of a painless method of carrying out the death sentence (which doesn't seem to exist yet), so I think I'd bring back the death sentence when it's possible to do that, but not right now.