There are 923 words that break the "i before e" rule. Only 44 words actually follow that rule.
This is a picture circulating right now, claiming that a huge majority of the words break the "i before e" rule, and that only a few actually follow it.
Is the rule as often incorrect as the picture claims?
"I before E, except after C" is a mnemonic rule of thumb for English
spelling. If one is unsure whether a word is spelled with the sequence
ei or ie, the rhyme suggests that the correct order is ie unless the
preceding letter is c, in which case it is ei.
It won't be possible to skeptically analyze whether or not the rule is useful. I will stick to analysis of the factual claim. I'm assuming that the "i before e" rule is exactly as you've quoted from the Wikipedia article.