How much iron would I have to shoot into the Sun to blow it up? My understanding--though it's from a Science Channel show so I'm not sure if it is correct--is that there is a fusion reaction happening in the center of the sun. Atomic nuclei are being created and fused into higher atomic weights from lower atomic weights. By the time this reaction gets to iron on the periodic table (billions of years), the iron atoms are too heavy to allow the reaction to continue, so the star collapses and goes supernova within a short time.
Is this true? If so, can a comet made of iron enter the sun's core and destroy it? How much iron would it take? Or do I just have an inaccurate understanding (entirely possible).
Note: I do not intend to try to destroy the sun.
 A: First, a minor correction: iron is not too heavy to allow the reaction to continue, it is incredibly stable and therefore cannot produce anything else (it would take $\sim10^{22}$ years for it to decay into chromium and its binding energy is the highest per nucleon, so it would "cost" more to produce something heavier than iron has in it). Research shows that once silicon is produced in the core (silicon produces iron), the star has about a week before it blows up!
However, in order to produce that in the core, the sun needs to be about 6-8 times our suns mass. So rest assured that our sun will not go supernova (though it will go through a red giant phase and swallow earth in about 5 billion years).
The boiling point of iron is about 3000 K (5000 F) while the surface temperature of the sun is about 5500 K (10,000 F), so this comet-of-iron would evaporate en route to the sun's surface.
A: No, it is not true.  This is not how fusion in stars like the sun works.
The sun is fusing hydrogen to make helium.  At this point any other reactions are very rare, not sustaining, and irrelevant.  It is not true that a whole chain of higher elements are being created at this point.
It is also not true that iron is too heavy to allow nuclear reations.  Iron happens to be the low-energy point, so there is no net energy gain by fusing it with other elements, or fissioning it into other elements.  It is possible to get energy by fissioning much heavier elements than iron, like uranium and plutonium.
After the sun has used up its hydrogen and is mostly a ball of helium, it will first collapse a little.  This heats the helium so that now it can fuse.  This releases more power than the original hydrogen fusion did, so the sun expands to become a red giant, which as one of its side effects will engulf and incinerate the earth.
When the helium runs out, a whole sequence of other things happen.  For stars of the mass of our sun, there won't be a supernova, although there will still be a sizeable bang before the nuclear reactions cease and it cools down and becomes a dwarf.
A: Not at all. First of all, about 0.014 of the sun's mass is composed of Fe. If you do the math, you will realize that is over 4660 Earth masses of Fe in the sun. This is because the sun is a relatively high metallicity star (population I) and was likely formed in a zone entrenched with supernovae products. If you just look at the constitutents of the inner planets, asteroids, and meterorites, this is in line with what would be expected. 
If a "large" mass of Fe (comets don't contain much metal but we could replace your proposed comet with an asteroid of similar dimension) was to fall into the sun, it would just completely vaporize. The sun's temperature at the surface is ~5778 Kelvin which is much higher than the boiling point of Fe, Ni, or any alloy of the Fe-Ni. The atoms would disperse and would become lost in the sea of H and He nuclei, and wouldn't conceivably come anywhere near the core in one piece. Literally nothing about the sun would change in this scenario. Metal-rich objects (small ones) likely fall into the sun all the time and aren't detected. 
Now for some comments on fusion. The sun first of all won't ever fuse Fe in it's core as it simply isn't massive enough to do so. The temperatures required to fuse increasingly heavy nuclei have to increase enormously and this is aided by the core contracting and heating from the enormous pressures and masses pressing down from above. The sun simply doesn't have what it takes.
Also, Fe doesn't fuse not because the nuclei are too heavy. Fe in a massive core will indeed fuse into Ni and could go conceivably further. The problem is that these reactions are endothermic meaning they will absorb energy. At this point too, the temperature is so high that photons are able to split Fe and Ni nuclei apart back into lighter nuclei and individual nucleons. All of these processes will take energy out of the core. The less energy in the core, the more it will contract, the hotter it will get, and energy is lost faster until the core succumbs and collapses. Note that this is not an instinteneous event happening just from the presence of Fe. As the core collapses further, protons and electrons find it energetically favourable to form neutrons (neutronization), which takes more energy. 
I'm assuming you watched a program where they said that "iron is a star-killer" or some other dramatic nonsense like that. Remember that shows on television are made with entertainment value in mind and will simplify or simply misinterpret things for a general audience. Always watch with skepticism. 
A: I think I caught that show on the science channel too and I think they represented that particular point poorly.   First, I'm quite sure the sun already has a healthy amount of iron in it already, because all the inner planets do.   There's no logical reason why the sun wouldn't.    Iron is reasonably plentiful in the universe.    What happens when a star's iron core contracts and the star goes Super-Nova probobly requires pretty large iron core - maybe bigger than Jupiter.   Now, I'm just guessing, and it probobly has something to do with the purity of the iron core as well as the mass, but it probobly takes an enormous amount.   A whole lot more than 1 comet would bring.
Now, I suspect the sun doesn't has an actual iron core either, cause at those temperatures, everything is a plasma just kind of flying around and bumping into other elements, so, basically, if you were to throw an iron frying pan into the sun, the iron becomes a gas and it blends in with the other gas inside the sun not unlike how gas mixes up in our atmosphere.  
A: First, the other answers are correct that your understanding of the processes inside the sun is flawed.
Secondly, I believe that the other answers are fundamentally wrong regarding shooting iron into the sun to cause it to explode.  I am confident that shooting a large enough amount of iron into the sun would cause it to explode.  Basically, an object with a mass of three times our sun will collapse and part of the matter will explode unless it is supported by nuclear fusion.  If you had two solar-mass objects on opposite sides of the sun and they were not in orbit, or moving relative to the sun, and you allowed them to fall into the sun then you would have an object with three solar masses.  But even though the two large in-falling objects would cause substantial disruption to the core of the sun, they probably would not disrupt the fusion enough for the sun to explode and for the remnant to collapse into a black hole or neutron star.
Suppose that instead of 2 objects fired at the sun, you had 100 objects, each with one solar mass.  Each of those were fired from the same distance from the sun, and each object equally spaced so that their mutual gravitational attraction is not a factor in keeping them from hitting the sun.  Having 100 solar masses of iron impact the sun would probably be enough to break apart the areas of fusion or alternatively, cool the sun enough so that you would no longer have enough sustained fusion to support the sun (and the added iron) from collapse, and so the sun would explode and the remnant would collapse into a black hole.  I expect that it would take far less than 100 times the solar mass of iron to accomplish this, but I have no idea the actual amount required.
