We have conducted two pilot surveys for radio pulsars and fast transients with the Low-Frequency Array (LOFAR) around 140 MHz and here report on the first low-frequency fast-radio burst limit and the discovery of two new pulsars. The first survey, the LOFAR Pilot Pulsar Survey (LPPS), observed a large fraction of the northern sky, ∼1.4 × 10 4 deg 2 , with 1 h dwell times. Each observation covered ∼75 deg 2 using 7 independent fields formed by incoherently summing the high-band antenna fields. The second pilot survey, the LOFAR Tied-Array Survey (LOTAS), spanned ∼600 deg 2 , with roughly a 5-fold increase in sensitivity compared with LPPS. Using a coherent sum of the 6 LOFAR "Superterp" stations, we formed 19 tied-array beams, together covering 4 deg 2 per pointing. From LPPS we derive a limit on the occurrence, at 142 MHz, of dispersed radio bursts of <150 day −1 sky −1 , for bursts brighter than S > 107 Jy for the narrowest searched burst duration of 0.66 ms. In LPPS, we re-detected 65 previously known pulsars. LOTAS discovered two pulsars, the first with LOFAR or any digital aperture array. LOTAS also redetected 27 previously known pulsars. These pilot studies show that LOFAR can efficiently carry out all-sky surveys for pulsars and fast transients, and they set the stage for further surveying efforts using LOFAR and the planned low-frequency component of the Square Kilometer Array.