I'm just curious, because although they remained neutral, they are in Italy, which was bombarded during WWII. I was wondering if they took any damage (accidental or otherwise).
The Vatican was hit by bombs twice during the war, once in November of 1943 and again in March of 1944. The second bombing was done by an Italian plane, it killed one person and damaged the Pontifical Urban University and the Palace of the Holy Office with small bombs.
The 1943 bombing damaged the Vatican Gardens but caused no casualties. The supposition for years was that it was a lost American bomber. A 2010 book alleges that it was an attack on Vatican Radio made by fascist (and anticlerical) Italian forces. This book has not been reproduced in English, but there were contemporary rumors that an Italian plane was to blame. The RAF has also been blamed. The Vatican investigation into the bomb fragments yielded no clear culprit.
In any event, neither bombing caused major damage apart from the single death and another person wounded. It remains unclear whether the attacks were purposeful or accidental.