German Lopez says that "apostrophes offer an exciting opportunity to show other people how smart and educated you are"—which all by itself makes it worth learning how to use them. For example:
Another common issue is irregular plural words, like children and teeth. For these words, you add an apostrophe and an s — so children's toys and teeth's roots.
Live by the apostrophe, die by the apostrophe. My middle-school English teacher beat into us that only humans can possess things. Animals too, I suppose. Or countries. But in any case, never inanimate objects. So it's "roots of teeth," because teeth don't own roots.
Of course, some young punks think this is a dated rule that makes no sense, and they go around merrily giving inanimate objects possession of everything. This is appalling. Of course this rule makes no sense, but that's the whole reason that good grammar demonstrates how smart and educated you are. If we did what made sense, we'd eliminate the apostrophe entirely since it's never necessary for comprehension. But that way lies anarchy.
Anyway, everyone1 loves to argue about grammatical minutiae, so have a beer and get to it in comments.
1Actually, not everyone. But my readers sure seem to like it!