Fair market value for charitable donations. Get the market value from either ebay sales of used similar items, garage sales, etc. Also, if you drive to a charity to help them, like a church event, soup kitchen, etc., you can deduct 14 cents per mile driven each way.
On a federal level for rent, you cannot write it off. If property tax is included in the rent, then you can write that part off. If not, the landlord gets 100% of the property tax deduction.
On a state level, if your landlord does not include it as a line item on your rent, some states allow you to deduct a percentage of rent as if it were property tax, but it depends on the state. Most state tax programs like TurboTax and such will determine this part out for you.
If you use an area of the apartment, condo, duplex or home you rent for business, like a spare bed room for an office, or a portion of the living room dedicated to it, measure the square footage. Whatever that square footage is as a percent of the entire square feet of the dwelling, you can deduct that as a business expense. Same thing with the portion of your utilities (electricity, phone, internet, etc) you use for business.
If you have renters insurance, you can deduct that.
If something is stolen from you, you can deduct the fair market value as a loss, depending on what was stolen.
If health insurance premiums are more than 10% of your adjusted gross income, you can deduct the amount over 10%.
If you itemize deductions, you can deduct sales tax. Keep ALL your receipts if you do, it adds up!
Job hunting costs.