No Guns Required
One example may be the Rwandan genocide, which has been carried out in large part with machetes (apparently, purchased in bulk from China).
As for the Virginia Tech shooting, according to the official statements Cho fired over 170 rounds from a .22 (Walther) and a 9mm (Glock) semiautomatic handguns in about 9 minutes. Other sources estimate that he had 7 magazines for his Walther and 2 for the Glock: this means that Cho had to manually reaload his magazines at some point - and he could do so without being confronted.
At Columbine, instead, Harris and Klebold carried a variety of weapons, but interestingly no full-auto firearms. What they had, instead, was plenty of homemade bombs of various types. They also used sawed-off shotguns shorter than 26 in., which made them illegal under existing laws.
Anyway, there is another recent story of a massacre perpetrated without guns, but only with a bladed weapon (at least, if reporting is accurate): a man in the Samar province of the Philippines went on a rampage*, killed 10 people, among them many children, and wounded 14 others before surrendering to another villager. The article describes the weapon as a "21-inch-long knife", but I speculate that it may have been something different, a parang or a bolo perhaps (this is, admittely, a minor point).
But then, the response of the lefty elites would be to ban knives too - actually they have already done it.
Note: The post title has been changed from "Guns Required" on 8 Jun.
*It is an altogether different language, but the Malay/Bahasa Indonesia word mengamuk is fitting.