There are a lot of myths, internet rumors, and urban legends about super-volcanos - Especially Yellowstone. The truth of the matter is that geologists are not even sure if Yellowstone will ever erupt on continental scale ever again. In fact, there is evidence to suggest Yellowstone is dying volcano. A couple of things though…
While large magma chambers are certainly capable of producing large scale eruptions, they are also capable of producing numerous small eruptions. While Yellowstone is well known for its three “super-eruptions”, but it has also experienced quite a few smaller explosive eruptions, and several dozen effusive (think Hawaii) eruptions - as early as 70,000 years ago. If Yellowstone were to have another eruption, chances are it would be one of these small scale effusive eruptions. It might not even be big enough to close the park. In fact, the biggest eruptive threat in Yellowstone isn’t even magmatic, but rather phreatic explosions. (steam explosions) Because of the massive geothermal system in the park, phreatic explosions have been known to occur in the park three or four times a year. Another hazard many people don’t consider is the earthquake hazard. Yellowstone is also very tectonically active. It is more than capable of producing a 7.0 magnitude+ earthquake. One earthquake was so powerful it caused a landslide into a lake causing a Tsunami that wiped out a bunch of people on the other side of the lake. But what about a super-eruption?
It probably wouldn’t be as bad as people think it. A lot of films and TV have portrayed a Yellowstone Super-Eruption as some sort of America destroying apocalypse - but thats just not reality. While a super-eruption would be quite damaging, the USGS has actually run a simulation which predicts the majority of the damage would occur within 500 miles of the volcano, mostly due to ash fall. While that is still significant, it is not America ending by a long shot. More like a level or two up from Katrina. Even the much discussed “volcanic winter” may not be nearly as bad as we once thought. Some studies from the Toba eruption from 70,000 years ago (the one that supposedly caused the human genetic bottleneck. Google “Toba Catastrophe Theory” for ore info) suggest that the volcanic winter was only 1 - 3C drop instead of 5 - 7C drop. That would still be bad, but it would not be devastating. So in short, it would be bad, but you would likely survive it quite handedly.
If you want more info, the USGS has an entire department called the Yellowstone Volcano Observatory that goes into great detail about all of the geology behind Yellowstone.
Hope that helps!