Do we breath less oxygen in Humid air than dry air ? Since the volume of breathing remains same In rainy season, when Air is fully saturated, while we breath do we get less oxygen in than dry air ? Since the volume of breathing remains same?
 A: You are right that the higher the partial pressure of water vapor is in the air, the lower the partial pressure of the other gasses will be.
But this depends on temperature: when relative humidity is 100 % the partial pressure of water vapor may be lower than at 50 % RH and a higher temperature.

A: Yes, logically air which contains a high water vapour content must contain less oxygen and nitrogen per cubic metre. As a keep-fit runner myself I have sometimes pondered this problem, and wondered how many seconds or minutes it added to my running times, but was unable to come to any firm conclusions. Humid air also makes evaporation more difficult, so we overheat more easily in humid air than in dry air, and over long distances that in itself could slow one down.
A: If you would release liquid water in a closed system with air at a pressure of 1 bar, some of the water will evaporate until the partial pressure of water reaches the vapor pressure of 23 mbar (at 20°C). Since nitrogren and oxygen don't have a liquid phase at that temperature, the partial pressures add according to Daltons law, which means the total pressure raises to 1.023 bar while the partial pressure of oxygen stays the same. So you would get the same amount of oxygen.
In an open system like our atmosphere it is more complicated. Total pressure as well as partial pressures would want to equalize. What would happen probably depends on the exact dynamics of the atmosphere. But the partial pressures of water and oyxgen would still be seperate. If at one location the partial pressure of water is higher, water molecules will travel from there to locations with lower partial water pressure. However if gas phases act seperately like Daltons law suggests, why would those water molecules take oxygen molecules with them? Of course at the size of our atmosphere the equalization of pressures doesn't happen instantaneously. If we neglect the dynamics of the atmosphere, then the water partial pressure would just add to the total pressure at any location and disperse seperately. It isn't clear why the water would actually displace any oxygen, like the other answers suggest. If it is true that in areas with high humidity the oxygen partial pressure is usually lower, than this must be due to some atmospheric air flow somehow caused by the humidity, which would lower the total pressure. It isn't because water vapor displaces other gases.
There is another problem with this. The air we breathe is heated and humidified by our airway. When it actually reaches our lungs is 100% saturated with humidity, so breathing dry air versus humid air has no effect on the partial pressure of oxygen reaching our lungs. 
