The original silent “The Lost World” set the theme. So what’s your favorite monster rampage? When I was a kid I had nightmares of trying to hide in a labrynth from a hungry tyrannosaurus courtesy of The Valley of Gwangi. (see 2:42- 2:46)
King Kong going, er, ape is an all-time classic but I am a dinosaur fan so I’m going with the T.rex in The Lost World (JP2)
(*nitpick: it was an Allosaurus in Valley of Gwangi)
I always liked the Monster from the Id in Forbidden Planet. Stomping around invisibly, roaring as it shoves through that force field, and stands up to and is outlined in massed ray gun fire. Scary as hell when I was a kid.
Gojira, coming ashore in Tokyo, on the second night of his appearance in Tokyo Bay.
The T Rex & the SUV scene in the first Jurrasic Park is dynamite stuff.
The original King Kong, on the Empire State Building, still rates high.
I’m going with the Cloverfield monster.
The original movie monster was actually The Pet in the Winsor McKay cartoon of that name, circa 1921. As it grew larger and rampaged through the city it was bombed by zeppelins and biplanes. That makes it the first movie monster rampage through a city.
My favorite is the Rhedosaurus from Ray Harryhausen’s Beast from 20,000 Fathoms – it was the first 1950s “monster movie”, and contained all the elements that would make uyp that cliche. Only, since it did it first, they weren’t yet cliches. Also the first use of Harryhausen’s Dynamation/Dynarama technique, which significantly reduced the cost of such rampages. For film makers.
The Pet/The Giant Pet was adapted from this 1910 episode of his own Sunday comic, the Dreams of the Rarebit Fiend, but the appearance of the titular pet was completely changed, and it got MUCH larger in the cartoon (and meaner) and attacked a city before being hit by a bomb. The resulting explosion leveled the city:
The best monster rampage is the one that saved the city from the menace of the Killer Cars.
In An American Werewolf in London the protagonist and a friend are walking at night through the creepy moors and they start hearing this horrible roar getting closer and closer. Everytime they turn direction the roar still comes from in front of them. Suddenly in an instant the beast is upon them, slashing and evicerating in a terrifying fit.
Scared the beejesus outta me.
Another vote for The Beast From 20,000 Fathoms. Although Beast going beastly on the Evil Mutants in X3 also stands out. 
I’ll second the nomination for the Cloverfield monster (we had a name for it, but I can’t find the thread).
Also worthy of mention: the giant brown and green dudes from War of the Gargantuas.
The name I’ve suggested in these boards is “Rodney”, as in Rodney Cloverfield.
I know there was another suggestion, but I can’t remember it. And I’m not going to publicize it.
Snookum
That’s the one.
Gorgo and his mom did a fair amount of damage in and around London.