As with the Arabic and Chinese language families, different varieties of Romance languages are similar enough in syntax and vocabulary that speakers can kind of make themselves understood to each other if they speak slowly and choose their words carefully. Same with lots of closely related languages, e.g. German and Dutch. But they're not nearly mutually intelligible to the degree that American English and most varieties of British English are or that Hindi and Urdu are.
Regarding the Spanish/Italian example, the father of a friend of mine was fluent in Spanish, French, and Portuguese. Using an Italian grammar guide and his knowledge of Romance vocabulary from the other three languages, he learned Italian in a single flight from the US to Italy to the point where he was able to conduct business in Italy immediately upon landing.
I'm Dutch, and people from the east of Netherland don't understand why I don't understand German, claiming the languages are so similar. But I have real trouble understanding German. Maybe when it's someone from the north-west of Germany who speaks very slowly and clearly. People from the east of Netherland have much less trouble, somehow.
(I'm utterly unable to understand people from the Dutch province of Zeeland when they're speaking to their parents. That's complete gibberish to me, though it doesn't have a special status as a local language, as far as I know. (unlike Nethersaxon, for example))
When you have trouble understanding germans, are they speaking Hochdeutsch or Platt? I'm curious if Platt is more closely related to Dutch than Hochdeutsch or not.
As a german, I always have problems understanding other germans when they speak english, so there's always that ;).
I'm Romanian, as a kid in a few months I became fluent in Italian just from watching their TV channels, no dictionary involved. It was a mass phenomenon at the time since their TV channels were quite popular on cable.
Regarding the Spanish/Italian example, the father of a friend of mine was fluent in Spanish, French, and Portuguese. Using an Italian grammar guide and his knowledge of Romance vocabulary from the other three languages, he learned Italian in a single flight from the US to Italy to the point where he was able to conduct business in Italy immediately upon landing.