In RTS: When attacking a base that was already there, why is there any metal/ore/gold/whatever-resources left? You can build a base and strip mine it in under one hour, that enemy base was there for weeks at least. Or, if the resources are infinitely renewable: Why hasn't the entire map been covered by top tier units, that were payed for by mining the infinite recourses for 3 weeks straight.
In a fantasy rpg: Not only does no-one think of using phoenix downs or heals in cutscenes, no-one except your party seems to ever use them. If you arive at a village that has just been attacked and many people are dead or wounded, no-one will be using any items to fix it. Worse, sometimes there's still a shopkeeper in the town, STILL SELLING the potions.
As mentioned, stealth games: Why do guards keep assuming that it's nothing, even though they've seen you run passed several times, and have seen several of their commrades get knocked out/killed.