What are some examples of concurrent power between state and national governments?

Concurrent powers are those powers which are given both to
the national government and to the state governments.  These can be exercised separately
by the two levels of government.  Two important examples of this type of powers are the
power to tax and the power to build roads.

The federal
government and the state governments both have the power to impose taxes on the people. 
This is why we have federal and state income taxes in most states.  Both levels of
government have the right to build roads.  This is why we have interstate highways but
also state highways.

These are the two most important
concurrent powers.