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 × 10⁴ deg², with 1 h dwell times. Each observation covered ~75 deg² 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 deg², 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 deg² 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 re-detected 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.