What would someone of Italian heritage be considered as for purposes of race classification in the US, say for equal opportunity or school applications and such? Are they Hispanic? Latino? Both? White?
White.
White, almost certainly, if there isn’t a seperate category for them ( or something like “southern European” ).
Latino/Hispanic ( Hispania = Roman Iberia, including Portugal ) refers to Spanish-speakers. Even more specifically it more often refers to New World Spanish-speakers, as opposed to European Spaniards, though Spaniards are technically included. For some reason the term usually ( but not always, depends who you are talking to ) excludes Portuguese speakers like Brazilians.
- Tamerlane
The way I’ve heard it “Latino/a” is only used for New World Spanish-speakers, while Hispanic can be used for both New and Old-world Spanish speakers, more usually the former.
Is this right?
I had to fill in a similar field in a University form, so I asked for help to the University advisors. They told me that Italians are just considered white.
That’s certainly what I’ve always thought.
Hispanic = All Spanish speakers
Spanish = People from Spain
Latino(a) = Spanish speakers from South America
US census about definition of Hispanic. Setting aside the racistic way of categorizing people in races like black, white or Asian, it must be noted that in USA the term Hispanic/Latino is not a racial definition. Such a person can be of any “race”, it only refers to their Spanish origin. It’s an additional label, and those who identify as such must also provide their race. Thus an Italian from Italy is unquestionably white (unless of course they are black or from East Asia…).
It should be noted that US definition of terms Hispanic or Latino only includes people of majorly Spanish-speaking countries in America. It doesn’t normally include Brazilians nor Spaniards. In Europe the term Latin/Latino would probably mean either Latin American or someone from Romance-languages speaking (Latin) Southern Europe; depends on context. Thus you would theoretically describe an Italian as “Latin” but not really “Latino”.
However, regarding the American usage of these words, Wikipedia seems to agree with pasunejen, and it does explain why these labels are so confusing. Though it doesn’t answer whether an second-generation Italian immigrant in Buenos Aires moving to New York would be considered H/L in addition of being white. Probably not, if they don’t identify themselves being Spanish.
This reminds me of a humerous anecdote a guy I met once related - this guy was was a pretty swarthy looking person, of Italian ancestory, and one time he encountered two opposing gangs fighting each other - one white, the other gang hispanic. He stopped the fighting by yelling out “Which f*** side am I supposed to be on?” - all the gang memebers took a look at him, and broke out laughing. 
Italian-American checking in: we are officially White these days, although my grandfather (dark enough to be frequently mistaken for hispanic in San Antonio) has an assortment of stories from before we were considered such. I imagine an influx/rise to prominence of even-darker folks adjusted the curve to where the deep olive of a Calabrian tan is still pretty fair.
Actually from any part of America (Mexico, the Caribbean and Central America too).