If you are married and living with your spouse and/or minor dependents, you will have the option of living on-post or living off-post and receiving a monetary stipend known as the Basic Allowance for Housing (BAH). BAH is not classified as "pay", and therefore is not taxed like regular income. It is also paid to service members with dependents while they are in basic training or AIT.
At most Army posts, if you are single you must hold the rank of Staff Sergeant(E-6) to be allowed to live off-post, although some allow Sergeants(E-5) to live off-post if the barracks are crowded.
In addition to being non-taxable, BAH varies according to rank, dependent status (non-military spouses are considered dependents), and the area you (or your dependents) live. BAH is designed to cover around 96.5% of housing costs, although it based on what the Department of Defense considers "reasonable acceptable housing" for an individual or individual with dependents (although the number of dependents doesn't matter).
For soldiers and dependents stationed overseas, the Army provides Overseas Housing Allowance (OHA) which varies every two weeks, based on currency fluctuations.
You can see the current rates on the DoD BAH calculator. You can also find more information (including a breakdown of past years and the OHA calculator) at http://www.defensetravel.dod.mil/site/bah.cfm.