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When air is enriched with water, how much volume increase can be expected?

I am aware that the volume increase will not be proportional (i.e. $\pu{1L}$ air + $\pu{10mL}$ gasified water will result in a volume of less than $\pu{1.01L}$).

So how big is the volume increase actually?

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    $\begingroup$ At normal pressures, water vapor is pretty much an ideal gas, as is air. $\endgroup$ – Jon Custer Jul 7 '16 at 14:27
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The short answer is that the behavior of the system you describe should very well approximate that of an ideal gas at room temperature and 1 atmosphere, and that the addition of $\pu{0.01L}$ of water vapor to $\pu{1.00L}$ of air will give you a total volume very close to $\pu{1.01L}$ (assuming constant temperature and pressure).

The departure from ideal behavior for water vapor strongly depends on relative humidity. While the absolute humidity given in the question is only $1\%$, this would correspond to $100\%$ relative humidity at $\pu{6^oC}$, and greater than $100\%$ relative humidity at lower temperatures. Gas molecule interactions so strong that condensation occurs essentially represents the opposite extreme of the assumptions made for an ideal gas.

So, at the extreme of very low temperatures, essentially all of the water vapor would condense and your calculation would have a high bias of 1% if you were to assume ideal gas behavior. However, at room temperature (i.e. $\pu{20^oC - 25^oC}$) this will not be the case and the assumption of ideal behavior would introduce negligible error.

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