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I apologize before hand if I lose anybody here, but I'll step in as an engineer if I may. Also, as much as I'd like to cite my sources, I don't think any of y'all want to pay for $800's worth of engineering textbooks.
The collapse of WTC 7 makes complete and total sense from an engineering perspective. I'll list my arguments to make it a bit more readable.
1.) Buildings are designed to support their weight and any other kind of loads(i.e. dead loads, wind loads, snow/rain loads, etc.) in complete equilibrium. What this means is that all of the supports are responsible for upholding this loading and should any of the supports, especially 25% of the building be damaged or destroyed the building will fail and collapse in upon itself.
2.) The beams will already be subjected to all kinds of stress because of their loading. Stress is essentially force divided by cross-sectional area. Now, there are three kinds of stress that are important: normal stress, shear stress, and bearing stress. As the loads increase, especially if supports and the foundation start to fail, the stress in the remaining beams will increase as the load(force) they are supporting increases. As stress increases you the materials start to reach their "yield" points(as plotted on a stress curve) and begin to buckle, bend, etc. This only worsens the problem as the loading becomes even more assymetrical and increases on the remaining beams, said beams will quickly reach their failure point, where they permanently deform, snap, explode(more for timber), and fracture.
3.) While fire may not cause failure outright, it can lead up to it. As steel and just about every metal is heated, it becomes more ductile(malleable, can bend easily) and thus will deform under loading. Also, let us not forget that these fires were started by aircraft crashing into the WTC 1 and WTC 2, which means they were no doubt accelerated by jet fuel(I don't recall off hand what most commercial jet fuel is). This means they were burning at far higher temperatures than would other burn in a normal structural fire, which also means they were closer to the melting point of the steel. As you get closer and closer to that melting point, steel becomes more and more ductile, and will begin to deform far more easily than it would otherwise.
4.) WTC 7 did not collapse until after WTC 1 and WTC 2 collapsed. The energy from those two towers collapsing had to go somewhere. It was directed into all of the other buildings and objects surrounding it. As the building falls, the potential energy it has is quickly converted into kinetic energy. We'll just look at a single floor. As that floor falls it converts potential energy into kinetic energy and then when it impacts the ground it must then "find" a place for that kinetic energy it has to go. Some is converted into sound energy, the rest will cause the debris to scatter and explode, sending debris everywhere and causing damage in the surrounding buildings.
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"There is no need to suppose that human beings differ very much one from another: but it is true that the ones who come out on top are the ones who have been trained in the hardest school." -- Thucydides
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