The synthesis of esters from an alcohol and a carboxylic acid, is an example of a dehydration, though as chem_tr said, this is not the standard case, as H+ comes from the acid and OH- from the alcohol. Some alcohols (especially aldols) dehydrate quite easily into alkenes. Others dehydrate upon heating or in the presence of strong acids.
Dehydration is also used in the purification of organic solvents such as methanol. In such cases, dehydration may be achieved by fractional distillation.
As far as inorganic compounds go, 'dehydration' is simply the process of removal of water from hydrated crystals (that can be achieved by simple heating). Like mrjeffy's example, you can dehydrate crytals of copper sulphate, or calcium chloride or ferrous sulphate by heating them.
There are several other examples, but here's one :
Heating sulfuric acid produces some fumes of sulfur trioxide. Write down this reaction, and you'll see that it is a dehydration reaction.