"I came from Italy" or "I come from Italy"

Solution 1:

"I come from Italy" is the better semantic choice. "I came from Italy" refers to a more specific time frame: "I came from Italy last night." However, the more natural one would be "I'm Italian but currently live in the States."

Also, the past tense usually refers to an action that is 100% complete and done with; however, "I come from Italy" shows that the relation is still an existing one.

Solution 2:

It is:

I come from Italy.

Because you still do. You are alive and you originate in (present tense) Italy. You come from (present tense) there.

However, were one to talk about a dead person, a past tense would be used, like this:

My grandfather came from Italy, but is buried in USA.