Nothing. Rent and utilities, whether paid directly to a landlord or through a cost-sharing arrangement with a roommate or co-tenant, are considered personal expenses. As such, these expenses are not deductible for federal income tax purposes.
Some states have various credits for persons paying rent. These may depend on one's income or other factors and may have specific definitions of what payments constitute "rent." You should check with your state's Department of Revenue or other taxing authority for relevant instructions.