The statistical properties of fluid particles transported by a three-dimensional fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics are investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov time scale, th, up to one large-eddy turnover time. Our analysis reveals the existence of relatively rare trapping events in vortex filaments which give rise to enhanced intermittency on Lagrangian observables up to 10th. Lagrangian velocity structure function attain scaling properties in agreement with the multifractal prediction only for time lags larger than those affected by trapping