The massive drop in oil prices isn't even the biggest one in the last decade. The 2008 recession saw oil hit a similarly low level, but it started falling from a much higher peak, and on an even faster time scale. On a percentage basis, the price of Brent crude oil also saw many large drops between 1997 and 2002.
That suggests two things: (1) the markets have weathered storms like this before, and (2) prices could still drop before recovering. Here's a chart comparing oil and the S&P 500 over the past 20 years. (Funny enough, from a starting point in December 1995, both have gone up about the same.)