Will my passport get stamped in Italy or Spain?
 

I'm traveling to Italy and Spain on a Schengen Visa that was issued by Spain.

I'm flying on Alitalia airlines, so the plane makes a stop in Rome, before landing Barcelona. Will my passport get stamped in my Rome stopover or when I land in Barcelona?

The thing is even my departure is from Italy, so I'm worried that I will have nothing on my passport that proves I have been to Spain. What if the officials think I have ignored the rules, next time I apply for a Schengen Visa?

Both Spain and Italy are signatories to the Schengen agreement regarding immigration within Europe (not necessarily the eu as Britain and Ireland are not signatories while Switzerland is)...this agreement essentially does away with border controls among the signatory countries. So.

Upon landing in Italy you will go through passport control and your passport will be stamped by the Italian authorities as the entering point for I believe th3 60 days you are allowed in the Schengen area without a visa. Therefore when you fly on to Barcelona upon arrival you will not go through a passport control nor will your passport be checked or stamped (sometimes, very very rarely if there's some sort of emergency or they're looking for somebody they might look at passports but for the most part on intra Schengen flights they don't_. So now when you leave Italy on the way home, you will be stamped out of Schengen at the last airport in Italy I take it Rome...the flight that leaves the Schengen area determines where your passport is stamped out.

Therefore in the case you describe, you will have no Spanish stamp in your passport if that is important.

Italy is your point of arrival in the Schengen area, so your passport will be stamped there. They will check your Spanish issued visa. I assume you are staying longest in Spain, hence the visa from there.
Unless your visa is a multiple entry visa you cannot leave and re-enter the zone on your visa, but you can travel freely within the zone.

For those who can travel visa free they can stay for 90 days in 180, not 60 as xyz123 suggests.

90 days in, then 90 days out before coming back in (a quick trip to a non-Schengen country does not reset that clock).
As to where your passport get stamped - the original question - it doesn't matter, any Schengen signatory country acts on behalf of any other - in that respect it's almost like entering the US in any state and leaving the US from any other state.