Harry's Cloak of Invisibility is unlike any other - it is Death's own Cloak of Invisibility, according to "The Tale of the Three Brothers." Ron is the first to realize that the Cloak is unique: "I've heard stuff about charms wearing off cloaks when they get old, or them being ripped apart by spells so they've got holes in. Harry's was owned by his dad, so it's not exactly new, is it, but it's just...perfect!" (416-7). Dumbledore later confirms this pronouncement, "It was a Cloak the likes of which I had never seen, immensely old, perfect in every respect..." (715).
For being a powerful magical artifact, Death's Cloak of Invisibility sure does have a lot of catches and rules.
Yet, this statement is a little misleading and confusing. It means simply that the Cloak itself cannot be damaged by spells, not that the wears are immune as well.
We see the Cloak unaffected by magic when a Death Eater attempts to summon it when Harry, Ron, and Hermione are hidden underneath it in Hogsmeade. "Harry seized its folds, but it made no attempt to escape: The Summoning Charm had not worked on it" (555).
However, there are multiple instances where Harry is frozen while invisible underneath the Cloak. First, Draco's spell, then later Dumbledore's.
Perhaps most importantly though, Harry acknowledges hiding underneath it could not have saved his family: "The Cloak couldn't have made them curse-proof" (715).
Tune in tomorrow for J is for J.K. Rowling!