Why search for and track NEOs at all? After all, the Earth is still pelted regularly by leftover bits from the Solar System's formation. As long as those bits range in size from dust-like to about 50 meters (164 feet) across, there's not much to worry about: the speed at which they enter the Earth's atmosphere typically causes them to burn up or disintegrate before impact.
But larger NEOs? We have a reason to worry about the danger they pose upon crossing our path.
For example, an object a little more than 50 meters in diameter could devastate any community in its immediate path (the 1908 Tunguska impact event might be one instance of a collision with an object of this size). On the other hand, if an NEO that size landed in an ocean area, it could generate powerful tsunamis with deadly results for coastal settlements.
NEOs on the order of one kilometer or so across would be even more cataclysmic upon impact. An object that size could cause massive firestorms and blast huge amounts of debris into the atmosphere, leading to acid rain, blocked sunlight and a severe threat to plant (and, by default, animal and human) life around the globe.
For impacting NEOs larger than that? Don't ask. Cosmic objects that are 10 kilometers or more in diameter have "extinction-class" potential upon impact, according to scientists.
The good news is, there are fewer large NEOs than small ones, meaning the possibility of a catastrophic or extinction-class impact in our lifetimes is small. The bad news is, impacts large and small do happen over time which is why NASA continues tracking thousands of objects.
While objects between 5 and 10 meters across hit the Earth about once a year, one-kilometer NEOs tend to strike about once every 500,000 years. The last extinction-class sized object to hit us was probably the asteroid that struck what is now Mexico's Yucatan Peninsula about 65 million years ago. The effects of that collision are believed to have contributed to the massive die-off of dinosaurs and other plant and animal species of the time.