Basic Trope: Monsters and other villains tend not to be hurt by firearms.
Straight: Bullets fired at the monster are shrugged off.
Exaggerated: The monster shrugs off not only bullets, but also grenades, artillery shells, and tactical nuclear weapons.
Only special bullets are effective against them.
The monster may not be outright immune to bullets, but when it needs a whole magazine to kill one, 30 rounds might as well as be 30,000 in a tense close quarters fight where it can tear a man in half like wet tissue.
The monster is incorporeal, so of course guns can't hurt it.
Alternatively, it has a million hit points.
Or: It's a huge monster with thick skin. The bullets barely penetrate, and, even if they did, the scale is just so massive that a normal-sized bullet can't do any real damage.
"This is the most powerful gun in the world. Nothing is immune to this baby."
Alternately, a scientist makes his monster possible to kill with bullets because a killing machine was not his intention (or because he's worried about his killing machine turning on him).
Discussed: "You know how the monsters in all those disaster movies are always immune to bullets? That's not entirely inaccurate..."
Conversed: "Geez, why do those guys in disaster movies always shoot at the giant monster? It never works!"
The uselessness of bullets leads to an increasing reliance on heavy weaponry by the monster hunters, which in turn breeds monsters who are even tougher, creating an escalating cycle of violence and lots of collateral damage.
Casualties and quitting among law enforcement officers and soldiers skyrocket because their weapons are useless against the monsters, leading to even more depression and fear.
The monster is only one of several antagonists, the rest of whom are not bulletproof, making that monster a special threat.
Another option is that the monster gets stronger, but the heroes are adaptable and intelligent, leading to a Lensman Arms Race.