Grammar lesson, version 2.0
Howard Scrimgeour wrote and reminded me that the issue with apostrophes in possessives isn't related to gender, it's the fact that pronouns are a special case. So I've made a few changes. Lines 7 and 8 have been reworked completely, and line 12 uses "neuter" instead of "neutral". I also decided to rewrite line 5 to eliminate the dangling participle - this is about grammar, after all - and made a small tweak to line 1.
While apostrophes are useful when you're forming a possessive
The ability of English to confuse things is impressive
(You'll have noticed, if you're neither unobservant nor myopic
That they also form contractions, but that's quite another topic)
If you're writing about objects that belong to Bill and Sue
Then "Bill's" would be a proper form, and "Sue's" is valid too
But that form's not universal, and you're sure to come a cropper
If you use it when the noun is pro, and not common or proper
For the lesson is that less is more, and more is surely less
When you place a stray apostrophe between "i t" and "s"
And though trying to remember this odd rule may give you fits
When the neuter pronoun owns a thing, it isn't "it's", it's "its"