I just recently answered a question on when coins started portraying heads.

The reason why is because the Romans would use coins as a showplace for propaganda. The coin would often feature the emperor on the obverse (front, heads side) and a great achievement of his on the reverse.

The custom was continued as nations kept depicting a ruler or someone important's head on coins.

The bank notes in Brazil have animals instead of people.

One additional reason, at least according to this source from an old "How Money is Made" broadcast, is attributed to humans being accustomed to looking at faces; thus, if we are familiar with a particular piece of money, it is theoretically easier to notice counterfeits via improper printing of the face.

(note: I couldn't find a location in the video that identified the person talking about this - I assume he is a US Mint representative, but I only remembered this quote being made in this video)