When #""^1H# #NMR# experiments are performed, the diamagnetism of all #""^1H# nuclei in the SAMPLE are interrogated. If we use solvents that already contain #""^1H#, then these signals WiLL DOMINATE the spectrum. (Why? because of their concentration.) Sometimes, a solvent can be used that contains few #""^1H# nuclei, i.e. per-fluoroacetic acid. The chemical shift of the proton here would occur well downfield, leaving a window for the desired spectrum.
Modern NMR spectrometers also use the deuterium signal as a means to lock the frequency (the deuterium frequency is thus the reference frequency; mind you, these days, magnetic fields tend to be very stable, and spectra can often be run unlocked).
Of course, #""^31P# and #""^11B# NMR spectroscopies are now routinely performed. Researchers in these fields often add a small quantity of deutero solvent to their reaction mixture, and do the experiment for the heteroatom (in which the proton resonance will be invisible, why?).
Deutero solvents (apart from chloroform-d) tend to be horrendously expensive, and the more expensive ones (i.e. #"toluene"-d_8#, #"methylene chloride"-d_2#, #"THF"-d_8#, #"benzene"-d_6#) tend to collected after an experiment, and then recycled by distillation (which of course is a very good practice both in terms of economy and the environment).