Many different technologies have been developed to measure magnetic field strength. Luca Bottura of the CERN classifies these technologies according to the range and accuracy they cover:

Only fluxgate and Hall devices have at this time found widespread commercial acceptance: fluxgate devices in low-field applications such as magnetic compasses, and Hall devices in a very broad spectrum of medium field industrial and laboratory applications.
Metrolab masters three magnetic measurement technologies, covering the high-field, high-precision quadrant of technologies:
For slowly varying, uniform fields above about 10 mT, Nuclear Magnetic Resonance (NMR) is the gold standard of magnetic measurements, providing much better than 1 ppm resolution with practically no drift. Electron Spin Resonance (ESR, also called Electron Paramagnetic Resonance or EPR) provides similar performance at lower fields.
Fluxmeters integrate the voltage in a moving coil in a static field, or a static coil in a varying field. This is a time-honoured and extremely flexible measurement technique, suitable for a wide range of field strengths, geometries and frequencies.
Three-axis Hall Magnetometers are easy to use and provide reliable, medium-precision measurements of all components of the magnetic field at a single point.Besides the basic measurement technology applied, choosing the best magnetometer for your application should include many other criteria: