A Measurement-while-Drilling method and apparatus for obtaining information about a formation uses sensors on substantially non-rotating pads attached to a rotating housing that is part of the drilling assembly. The pads make contact with the formation. The sensors may be density, NMR, resistivity, sonic or electromagnetic. The NMR sensors may use a static magnetic field that can be either radial or longitudinal in direction. The resistivity sensors may involve direct measurement of leakage current or may rely on induction methods. The sonic sensors may be three component transmitters and/or receivers for determining compressional and shear velocities of the formation and may also be used to image the formation in a VSP or a reverse VSP. In an alternate arrangement, the sensors rotate with the drill bit. A downhole microprocessor analyzes the data to improve signal-to-noise ratio and to reduce redundancy in the acquired data. Depth information may be telemetered from an uphole controller to facilitate the process. The downhole processor has adequate memory to store the processed data for subsequent retrieval when the well is being tripped. Alternatively, a subset of the stored data may be telemetered uphole during the drilling process.