"Will I be able to enjoy a vacation in Italy if I don't speak or understand Italian?"
I have been asked this question several times by people who have enjoyed hearing about my trips to Italy, but were nervous about traveling there themselves because they do not speak Italian. Truth be told, I speak very little Italian myself and have gotten along perfectly fine in most of my travels in Italy. There have only been a few isolated incidents and places where this was not the case, but not to such an extent that it interfered with my enjoyment of my vacation or caused me any real hardship.
In general, you will find that it is very easy to get along in major cities in Italy (such as Rome, Florence, Venice and Milan) even if you don't speak Italian. Tourism and international business are major industries in these cities. Therefore most shop owners, hotel and restaurant staff members, museum and church guides, and transportation operators have basic proficiency in German, French, Spanish - and yes of course, English! Signage is typically provided in multiple languages, and menus available in both English and Italian.
Language issues are much more likely to arise if you are traveling to smaller cities or rural areas of Italy. In such places, speaking Italian may be much more necessary in order to get around easily, order in restaurants, or make purchases in shops. If you would like to visit such areas - even just on a day trip while staying in a larger city - consider traveling with a local Italian guide or large tour group instead of on your own. You can often make such arrangements in advance, or via your hotel upon your arrival in Italy.
I would offer a few points of advice for tourists visiting Italy who do not speak fluent Italian: