Jarring indeed to a G.O.M. like me.
It's simple enough, folks:
- When "its" is a possessive or genitive, it takes no apostrophe. Just substitute "his" in the phrase and you'll see the use. Example: "Its eyes shone in the darkness."
When "it's" is a contraction of "it is," it takes the apostrophe. Example: "Baby, it's cold outside."
Late addition: See examples of apostrophe abuse here.