The two strongest factors which determine what your face looks like are your Sun Sign and your Rising Sign. Ofcourse there's more to it then just this, your face is further influenced by the affects of the aspects to your Sun and Ascendant, as well as the signs these aspecting planets are in. Other factors may also come into play in a lesser way.

Nationality also plays a role, this is because each nationality is affected by it's own sign and ruling planet as well. For example, the French are very Libra like, they're big on things like diplomacy, being good lovers, fine art, etc... Libra is ruled by Venus, goddess of love, peace, beauty, and seduction, and this affects their general look and cultural values. The Russians are very Scorpio like, as a whole, they tend to be rather secretive, suspicious, competitive, and love to be powerful... Scorpio is ruled by Pluto, the planet of power and dominance.

Nevertheless, the affects of the Sun and Rising Sign can cause even two people of differing nationalities to look very similar.