There was a ton of giant bug/giant monster movies in the 50s, but the giant ant movie THEM! from 1954 is the clear standout. As radioactivity mutates ants in Los Angeles to become giant sized, they terrorize the city. What really sets this one apart from the rest is that it takes itself seriously, and has a pretty damn good script, to boot.
And if you pay close attention, you'll see a cameo appearance by Leonard Nimoy as a teletype operator, as well as a quick appearance by Bea Arthur lookalike Fess Parker.
The movie not only influenced other giant monster movies of the day, but elements of it have been used in later films like ALIENS, and STARSHIP TROOPERS as well.
The opening scene is pretty scary. Some police find an 8 year old girl who can't speak, and is in shock. She's seen something so horrific she just sits there wide eyed. And when she finally talks, she simply screams "THEM! THEM! THEM!". Only later do we find out what the hell she's talking about.
I really like this review from BrianG in the Internet Movie Database.
This is the granddaddy of 'em all, the film that pretty much started giant bug genre of sci-fi films and spawned countless imitators, none of which are remotely as good as this one. This movie has pretty much everything going for it: a literate, atmospheric, extremely well-written script for what is essentially a B picture (although Warner Brothers put a substantial amount of cash into it)l outstanding acting jobs by everyone from the leads on down to the extras; razor-sharp direction by an old pro, Gordon Douglas (by far his best film; nothing he did before or since was anywhere near as good); a combination of visual and sound effects guaranteed to creep you out (the scene where James Whitmore's partner goes outside the wrecked store to investigate the strange noises he hears is among the scariest things you'll ever see). Also, the characters are believable; they act like you know people would act in the same situation.
Edmund Gwenn isn't the typical befuddled scientist you see in these films; he may be a tad distracted at times, but he gets down to business when the situation calls for it. Joan Weldon, his daughter, isn't just just a pretty face for the leads to fight over; she's every bit as much a scientist as her father, and she lets that fact be known right away. There's another level of this film that works well, too; comedy. Not the slapstick kind, or the stereotypical dumb cop or cook or crew member (usually from Brooklyn) that pops up in these films, but there are several lighter moments in the film that really work. Everyone remembers the wonderful Olin Howlin, the guy in the drunk tank who sings "Make me a sergeant in charge of the booze!", but there are several other segements that are equally as lighthearted; the great Dub Taylor playing a railroad detective suspected of stealing a load of sugar from a railroad car that the ants have actually done ("You think I stole that sugar? When was the last time you busted a ring of sugar thieves? You ever heard of a market for hot sugar?") and another scene in the drunk ward where a patient looks at the army major accompanying Arness and Whitmore and says, "I wanna get out of here, general, but I ain't gonna join the army to do it!" The special effects are first-rate but do not overwhelm the story, as is all too common in many of today's action films (that is, when there actually IS a story).
There are some truly terrifying scenes (the one where the ants, who have hidden in the hold of a cargo ship at sea, attack and slaughter the crew), and I liked the fact that the ants aren't invulnerable--they CAN be killed (it just takes a lot more effort)--and also that they actually act like ants. All they're doing is just what real ants would actually do--which makes things even scarier, given that we know how single-minded and vicious real ants can actually be.