The general trend these days is to get tough on crime.  Policies such as "three strikes and your out" are examples of this philosophies.

This amendment of the Bill of Rights discusses the right to bear arms.  There is some conflict over the interpretation of this amendment.  The NRA interprets it literally, meaning that you have a right to own a gun without restrictions.  Others see this as a right to form a militia.

Both the 8th and the 14th Amendments are brought up in regards to capital punishment.  The 8th due to the cruel and unusual punishment (what can by more cruel than death?).  The 14th due to the equal protection clause.  There is an apparent inequity in how capital punishment is given out.  African-Americans are statistically more likely to receive the death penalty.

These both look at crime as a result of social and economic conditions.  Therefore, if you can provide opportunities, then people would not turn toward crime to make ends meet.