We seek evidence of the Yarkovsky effect among Near Earth Asteroids (NEAs) by measuring the Yarkovsky-related orbital drift from the orbital fit. To prevent the occurrence of unreliable detections we employ a high precision dynamical model, including the Newtonian attraction of 16 massive asteroids and the planetary relativistic terms, and a suitable astrometric data treatment. We find 21 NEAs whose orbital fits show a measurable orbital drift with a signal to noise ratio (SNR) greater than 3. The best determination is for asteroid (101955) 1999 RQ36, resulting in the recovery of one radar apparition and an orbit improvement by two orders of magnitude. In addition, we find 16 cases with a lower SNR that, despite being less reliable, are good candidates for becoming stronger detections in the future. In some cases it is possible to constrain physical quantities otherwise unknown by means of the detected orbital drift. Furthermore, the distribution of the detected orbital drifts shows an excess of retrograde rotators that can be connected to the delivery mechanism from the most important NEA feeding resonances and allows us to infer the distribution for NEAs obliquity. We discuss the implications of the Yarkovsky effect for impact predictions. In particular, for asteroid (29075) 1950 DA our results favor a retrograde rotation that would rule out an impact in 2880.
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