A tenant may be entitled to reduce his rent or even withhold it altogether under limited circumstances:

(1) The landlord fails to meet his duty to repair the premises

Not all duties of repair fall on the landlord; some of them may fall on the tenant depending on local law and the terms of the lease. Nevertheless, to the extent that the landlord does have a duty to repair, the tenant may NOT repair the condition himself and deduct it from his rent unless his jurisdiction has enacted a "repair and deduct statute" (many of them have, however, and the number is increasing). Even under a repair and deduct statute, a tenant may not repair at a cost greater than one month's rent, refuse to pay the rent, and then bill the landlord for the balance. The tenant is also not allowed reduce the rent without making repairs on the theory that the unrepaired condition reduces the value of the property.

Note that just because the tenant cannot repair and deduct does not necessarily mean that he can't sue the landlord - repair and deduct statutes were designed to make it easier for the tenant to obtain relief without having to go to court.

(2) The landlord breaches the "implied warranty of habitability"

The implied warranty of habitability is a legal standard that requires a landlord to keep the premises in livable condition (in compliance with local building codes). It is "implied" because the law will hold the landlord to this obligation even if he makes no such promise in the lease. In many jurisdictions the tenant is theoretically not entitled to "repair and deduct" but must sue the landlord. Because the issue is habitability, the breach must be fairly serious - in jurisdictions without repair and deduct statutes, the landlord's duty to meet building code standards falling short of conditions that make the premises unlivable is the government's business, not the tenant's, and the tenant cannot sue on such violations but can only report the landlord's violation to the authorities in hope that the condition will eventually be repaired.

Neverthless, the tenant will often repair and deduct anyway as a matter of strategy, in order to force the landlord to go to the trouble of suing. The tenant will then defend the lawsuit by claiming that the landlord has breached the implied warranty of habitability, and the court will require the tenant to pay rent to the court, which rent will be returned to the tenant in whole or in part if he wins the case.