I recently took a part-time job at my apartment building and I am compensated with a free apartment. I filled out a W4 when I took the job, but my manager is unsure if I will receive a W2 at the end of the year. Will I be taxed for the money I saved on rent?
In some cases rent-free lodging can be excluded from taxable compensation to the employee. The IRS Publication 15-b lists the conditions (in this publication, "you" refers to employer):
It is furnished on your business premises.
It is furnished for your convenience.
The employee must accept it as a condition of employment.
The first one seems to hold in your case, however the other two may or may not hold, depending on your situation. For example, you said you're compensated with a free apartment, but it matters whether you had a choice in that (e.g.: if you were offered money or apartment then it is taxable, but if the employer said that you must live on premises because you have to be immediately available any time of day or night - then it is not).