The 1040EZ is the simplest of the three tax forms, next in complexity is the 1040A (and then the 1040).
The only types of income you can list on Form 1040EZ are wages, salaries, tips, taxable scholarships or fellowship grants, taxable interest of $1,500 or less, unemployment compensation and Alaska permanent fund dividends. If you have income from sources other than these, such as alimony or dividends, then you will have to file your taxes on either Form 1040 or Form 1040A.
Most persons using Form 1040 or 1040A have additional forms they need to include in their tax return, or they have enough deductions to exceed the standard deduction. Having mortgage interest and property taxes are a typical situation where you might be able to benefit by itemizing deductions.