Hemoglobin leaving the lungs is generally near saturation (even at standard pressures)
The environment of the lungs increases the affinity of hemoglobin for oxygen via a basic biochemical mechanism known as allostery. Essentially this means that factors in the lungs causes changes in the shape of the hemoglobin molecule that ultimately result in increased "tightness" of its binding to oxygen.
Essentially, these factors are higher pH (relative to the tissue bed and secondary to lower pCO2), cooler temperature, and lower levels of a cellular metabolite called 2,3-bis-phosphoglycerate. These characteristics are generally the inverse in the capillary beds resulting in decreased affinity of hemoglobin for oxygen (afterall, the oxygen wouldn't be very useful if the hemoglobin never let go of it so your cells can take it in).
Hemoglobin also exhibits "sigmoidal" kinetics with regard to oxygen binding. Hemoglobin exists as a tetramer, meaning it is four polypeptide (or protein) molecules bound togeather by non-covalent means (stuck togeather like magnets...not permanently). Once one oxygen molecule binds to one chain of the tetramer, the affinity of the tetramer for oxygen increases, again through an allosteric mechanism. This affinity increases even more as oxygen molecules successively bind, until the tetramer is saturated by 4 molecules of O2 and can bind no more.
Thus, any sample of blood will contain hemoglobin molecules that are completely saturated and those that are not. There will exist very few molecules bound to 1,2, or 3 oxygens (the majority either have 4 or 0). This is of course because the higher affinity molecules that are already partially oxygen bound, "steal" the oxygens from the less tightly bound molecules.
