When you see computer-generated images of asteroid 2012 DA14′s February 15, 2013 close flyby - showing the asteroid near Earth in space, seen from a distant vantage point - you might see the Earth, the asteroid, perhaps the sun, and maybe a few other planets. Here is another way to picture Earth and close-passing asteroids, from Armagh Observatory in Northern Ireland.

The image below is near-Earth space today - February 13, 2013. It shows all the objects currently within 0.3 AU of Earth - that's 45 million kilometers - or about 30 million miles - or about one-third of the distance between us and the sun. The red oval around Earth represents 3.84 million kilometers, or 10 lunar distances
© Computer-generated image via Scott Manley at Armagh Observatory
All asteroids currently within a third of Earth’s distance from the sun are shown, with Earth at the center, in pseudo 3D. The red oval around Earth represents a distance 10 times greater than the moon’s distance. View larger

Scott Manley was a PhD candidate at Armagh Observatory in 1998 when he created the software needed to generate this image daily (he now appears to be a software engineer in San Francisco). Please be aware that the image isn't depicting asteroids over some period of historic time. It's today's image, created with a computer program using data taken from from Ted Bowell's online catalog of asteroid positions and movements (Bowell is an astronomer at Lowell Obsevatory in Flagstaff, Arizona). Manley wrote of the image:
To represent the 3D nature of the positions every asteroid marked has its position projected onto the plane of the ecliptic (essentially the plane which the Earth's orbit lies in). So the asteroid sits at the top (or bottom) of the 'flagpole' and the base of the pole shows where they would appear to be on the larger map of near Earth objects. In addition, the motion over the next 24 hours is represented by lines at the top of the poles.
How can we understand - and live with the idea of - the image above? One thing to remember is that space is much vaster relative to objects in space than this diagram perhaps indicates. I cannot tell you the exact scale of the area of space portrayed here, relative to the objects depicted. But I do know that, at this scale, the word Earth or the words 2012 DA14 are much, much bigger than the objects they represent. Perhaps Earth is a speck of dust at this scale, and the asteroids are microscopic? Something like that. At any rate, there is much more space out there than planets or asteroids, and that is why, contrary to your first impression after looking at this image, we are not being bombarded with asteroids once a year or so.