Protons on oxygen or nitrogen atoms are a little strange. They can show up anywhere between 2-6 ppm. Because protons on OH and NH are involved in hydrogen bonding, their chemical shift can change depending on the temperature and concentration of the solution. They are not always broad peaks. Sometimes they stay on the molecule enough to couple.

Usually, these peaks are broad, hump-like peaks. This is because the hydrogen atom disassociates from the OH or NH bond. It falls off and returns to the molecule, so there usually is not time for it to couple with other protons. 

One laboratory trick to help determine if a 1H NMR peak is from an OH or NH proton is to add D2O, heavy water, to the NMR sample.  D2O interacts with the OH or NH proton and the hydrogen atom and deuterium atoms switch to form O-D or N-D. The 1H NMR peak then disappears confirming OH or NH. Protons on carbon atoms will not trade with deuterium of D2O. A new peak will grow in the spectrum, though. HOD is formed in the reaction.