Italy is a multigenerational culture that doesn't tend to marginalize its seniors, and older people are treated with a great deal of respect and deference throughout Italy. But there are few specific programs, associations, or concessions made for them. The one exception is on admission prices for museums and sights, where those ages 60 or 65 and older will often get in at a reduced rate or even free. There are also special train passes and reductions on bus tickets and the like in various towns. As a senior in Italy, you're un anziano (una anziana if you're a woman), or "ancient one" -- consider it a term of respect and let people know you're one if you think a discount may be in order.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.