I usually hear that plants should be placed in working areas to supplement the higher oxygen needs of working humans, or on the other hand, that should never be grown in bedrooms because they drain oxygen for their own respiration during night.
I somewhat doubt this is significant in comparison to natural variation in oxygen flow from the outside...
You are correct that the effect on oxygen levels are not significant. There is a much greater impact is on CO2 levels. Still, with respect to the effect on indoor air quality, the most important influence of plants is the removal of a class of pollutants known as volatile organic compounds (a.k.a. 'fumes') that include formaldehyde (Kim et al, 2010, Tarran et al 2007, Aydogan et al 2011. Plants also substantially reduce CO (carbon monoxide) (Tarran et al 2007).
Regarding the effect of plant respiration on air composition, it is also important to note that plant respiration is primarily affected by temperature, and occurs all day and night. However, during the day, the CO2 released by respiration is much less than the CO2 taken up by photosynthesis - otherwise the plant would have a negative carbon balance and eventually die.
For each unit of CO2 a plant takes up, it releases one unit of O2. However, the baseline concentration of O2 in the atmosphere is 20.95%, whereas the baseline concentration of CO2 is about 0.04% (NASA Fact Sheet).
Therefore, even if the plant converted all of the CO2 in the room to O2, the change in the percent would be from 20.95% to 21%. This would be difficult to detect. (Thanks to Oddthinking for pointing this out). Plant respiration rate is much lower than photosynthesis rate (otherwise they would have a carbon deficit and die) so the effect on O2 at night would be less than this.
Indeed, the presence of a person in the room would has a much larger effect on the O2 and CO2 in the room, and ventilation rate is the most important factor in maintaining a habitable atmosphere.
The most relevant citation:
Related reading not cited above:
