We focus low-power femtosecond laser beams with pulse durations down to 8fs onto a sharp field emission tip to generate electron pulses. We have observed either photofield emission (excitation of an electron and subsequent tunneling) or opitcal field emission (direct instantaneous modulation of the tunnel barrier due to the light electric field) depending on the laser power. Both processes are prompt, so that the electrons leave the tip within femtoseconds. The electron beam originates from an emission area as small as 2nm in diameter and has a divergence of down to 10 degree. These pulsed electron emitters could serve as efficient sources for time-resolved electron interferometry, for time-resolved nanometric imaging and for synchrotrons and novel accelerating structures.