The most famous NEA is 433 Eros that was visited by NASA's Near Earth Asteroid Rendezvous probe. A few hundred such NEAs are known, ranging in size up to four kilometers (km). Tens of thousands probably exist, with estimates placing the number of NEAs larger than one km in diameter at up to 2000.
Astronomers believe that NEAs only survive in their orbits for 10 million to 100 million years. They are eventually eliminated either by collisions with the inner planets, or by being ejected from the solar system by near misses with the planets. Such processes should have eliminated them all long ago, but it appears they are re-supplied on a regular basis. 
Some of the NEAs with highly eccentric orbits around the Sun appear to actually be extinct "short period" comets that have lost all their volatiles, and in fact a few NEAs still show faint comet-like tails. These NEAs were likely derived from the Kuiper belt, a repository of comets residing beyond the orbit of the planet Neptune. The rest of the NEAs appear to be true asteroids, driven out of the asteroid belt by gravitational interactions with Jupiter.
There are three families of NEAs:
1. The Atens, which have average orbital diameters closer than one astronomical unit (AU, the distance from the Earth to the Sun) and aphelia of greater than Earth's perihelion, placing them usually inside the orbit of Earth.
2. The Apollos, which have average orbital diameters greater than that of the Earth and perihelia less than Earth's aphelion.
3. The Amors, which have average orbital diameters in between the orbits of Earth and Mars and perihelia slightly outside Earth's orbit (1.017 - 1.3 AU). Amors often cross the orbit of Mars, but they do not cross the orbit of Earth. The two moons of Mars, Deimos and Phobos, appear to be Amor asteroids that were captured by the Red Planet. It is seen from the above that all Atens and Apollos have eccentric orbits that cross the orbit of the Earth, making them potential threats to our planet, while Amors do not cross Earth's orbit but some may come very close.
Also sometimes used is the Arjuna asteroid classification for asteroids with extremely Earth-like orbits.