Building a team and focusing on team building activities are viewed in different contexts. The secret of making a Team Building exercise work is to keep it as normal as possible and do not make anyone awkward. Do not assemble the team members and ask them what is their greatest source of worry. A vast majority of people would not like to mix their personal and professional feelings.
The best activities are those which the entire team feels proud in participating. Research points to the fact that when you help others, you tend to have more time on your hands.