The Census Current Population Survey / Housing Vacancy Survey tracks rental vacancies.
Using their time series / trend chart function on the Census page you can pull data. I got the following image showing rental vacancy rates nationally from 1956 to 2012:
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I don't know anything much about what drives rental vacancy rates at the national level. I assume part of it is building of new housing units versus growth of population.
Interestingly the national rental vacancy rate was relatively high even during the housing real estate boom. Vacancies were over 10% back in 2003 and 2004. It could be vacancies in rentals where high during the real estate boom due to individuals moving into single family houses instead.