What was the biggest volcanic eruption ever?

In recent history, the 1815 eruption of Mount Tambora has been the most violent volcanic eruption and also the most deadly, killing 92,000 people. This eruption also resulted in a major climatic change, causing what was known as "The Year Without a Summer". During the summer of 1816 Europe experienced frost and snow during the month of July, this caused widespread famine and crops worldwide to fail.

In the past 5,000 years, the "Taupo", New Zealand eruption was the biggest ever witnessed and recorded by humans. This occurred approximately 1800 years ago. The eruption lasted for several weeks and produced a sequence of pumice deposits which blanketed the landscape east of current day lake Taupo. Approximately 30km³ of pumice, ash and rock fragments were ejected in just a few minutes. These fragments travelled horizontally, as a liquid flow, and moved at speeds estimated to be somewhere between 600-900kmh. It crossed every obstacle in its path except the top of New Zealand's current highest volcano - Mt Raupehu. An eruption column 50 metres high was produced (twice as high as the 1980 Mt St Helen's eruption column), and the effects were seen in the sky as far away as Europe and China where records of it are still recorded to this day.

As for archaeological history, it's a toss up between the Toba Caldera, Sumatra Indonesia, which erupted approximately 74,000 BC, and the Huckleberry Ridge Tuff Eruption of Yellowstone Caldera, USA, which occurred approximately 2.1 million years ago.

In geologic history, it might be the the La Garita Caldera eruption in Colorado, about 28 million years ago, in the Oligocene Epoch. That put 5000 cubic kilometers of lava into play. There may be larger ones, but the farther back in time we go, the more geologic evidence is destroyed by tectonic activity.

Finally, it is likely that the most powerful eruptions ever were the Siberian Traps about 250 million years ago. The highest ranking on the volcanic scale is VEI 8; These are super eruptions. Yellow Stone and Lake Toba caldera were both VEI8's and Tambora was a VEI 7. But the Siberian traps would have been far off the scale. The Siberian traps were likely responsible for a mass extinction: the death of 95% of all life on Earth.