CB Insights:

We looked at all still-private unicorns since 2011 and charted them based on when they first joined the unicorn club. While initially the chart shows unicorns being created at a relatively calm pace, the rhythm accelerates noticeably in late 2013 (right around the time Aileen Lee wrote her famous post coining the term unicorn in November 2013). Since then, there has been an explosion in unicorn creation, with over 60 new unicorns in 2015 alone.

See also The Unicorn List (updated in real-time)