I think UNICEF does great work!! That said, it's main source of funding is US Federal government and UN (again, US).

As of 2007, around 60% of the funding was from government donors, 30% from private sector (including individual donations). The rest comes from organizations such as other UN agencies, NGOs, other international organizations.

In 2007 the US government contributed around 9% of the total budget.
Source(s):
UNICEF annual report 2007, http://www.unicef.org/publications/index_44268.html