Question

Why do we ignore the Earth's magnetic field when doing experiments; for example, running a current through a long wire and measuring the magnetic field it produces?

Answer 1

Because the Earth's magnetic field ranges between 0.25 and 0.65 Gauss, which is very small and can be discarded for the amounts associated with experiments are much higher normally. However your point is a good one and in some experiments or measurements it has to be taken into account beacause of the small fields involved or the accuracy of the measurement. One example can be Nuclear Magnetic Resonance, where the effect of Earth's magnetic field has to be taken into account