This neat little blog post at Real Clear Science covers some biological facts of human uniqueness and points out that social animals maintain physiological uniqueness even among very large populations.
And don't worry: though the world is growing more crowded, you will remain exceptional. UCLA researchers have found that in social species like ours, the larger the group, the more distinct its members. By focusing on alarm call vocalizations in eight species of social rodents, biologists Kimberly Pollard and Daniel Blumstein discovered that larger group sizes were strongly correlated to increased uniqueness. This made it easier to differentiate between individuals. According to Pollard:
Nature has solved the "Where's Waldo" problem by endowing highly social creatures with more unique features, which helps them find their pals in the crowd.