Plastic ground plug openings in 110 outlet broken
"Need" to be replaced? I'd say yes vs. leaving them indefinitely, just because overall when the outlet is fully intact it has its best chance at protecting you, and itself. 

Hypothesis on "why so many are broken":


person(s) yanked cords from their cord vs. unplugging correctly (maybe they had a 3 prong vacuum).
Or, are these outlets in places that furniture was likely placed right up against it?


Use caution while using them as maybe more is broken than what you see and consider changing them or having a handyman change them. As @EdBeal mentions, they are under a $1.00 each. And if backstabs are used, its a chance to "correct" that issue too.

FYI: Backstabs are where electrical wiring is pushed into a spring clip on the backside of a electrical outlet or switch instead of screwed on the sides securely.