In Google Spreadsheets, I need to use the COUNTIF function on a range with multiple criteria. So in the table below, I would need to have something like =COU
COUNTIF
=COU
You can also use ArrayFormula around a SUM(COUNTIFS()) construct:
=ArrayFormula(SUM(COUNTIF(B:B,{"Mammal", "Bird"}))
Source: Google Docs Product Forum