The video below, which uses data from the Asteroid Orbital Elements Database, presents a visual history of the asteroids discovered since 1980.
Two white numbers in the lower left-hand corner of the video indicate the year and the number of asteroids known to scientists at that time. Meanwhile, the animation shows the location of these asteroids within the solar system. (As the years pass, new discoveries are highlighted briefly in white. "Earth Crossers" are shown in red, "Earth Approachers" are in yellow, and other asteroids are shown in green.)
In 1980, according to the video, there were only 8,954 known asteroids. By 1990, that number had grown to over 14,000. The YouTube user that uploaded the video explains the new discoveries that took place throughout the 1990s:
As the video moves into the mid 1990's we see much higher discovery rates as automated sky scanning systems come online. Most of the surveys are imaging the sky directly opposite the sun and you'll see a region of high discovery rates aligned in this manner.
When the video ends in 2010, the solar system looks positively packed. Watch this amazing progression unfold in the video below.