I see a semi-regular appearance of the idea that the WTC7 building (part of the WTC complex but not one of the Twin Towers) collapsed due to deliberate demolition rather than due to damage from the Twin Tower collapses. This is pretty implausible so I did some internet research to find out why so many people believe it and what actually happened. I can say confidently that the reason belief is widespread is that real investigative sites are difficult to spot amidst the noise of offhand mentions of WTC7 and the conspiracies. The reason for the collapse can't be proven absolutely but strongly indicates failure of particular vulnerable cantilever trusses deep inside the building.
Why do so many believe the conspiracy theories? To find out, google up "WTC 7 collapse". You get pages and pages of conspiracy theories, interspersed with discussions of the entire WTC attack in which WTC 7 appears. Buried on pages 2 and 3 (they were much further back when I first checked this out) you find two gems with real engineering analysis:
The National Institute of Standard and Technology report (with an uninviting link, even)
and
Popular Mechanics' debunking of WTC myths
To give in idea of how the conspiracy broohaha has clogged up the memespace Wikipedia didn't mention either of these reports or their strong ability to explain details of the WTC 7 collapse.
Here is a hard-to-find complete video of the entire collapse from CBS. Notice the very left part of the penthouse complex falls into the building several seconds before the building collapses. The actual collapse start from the center, with the remainder of the penthouse complex coming down fractionally before the rest of the building.
Here is an easy-to find typical conspiracy video of the WTC 7 collapse. Notice it only covers the building as a whole coming down. You don't see the penthouse disappear earlier.
This is, of course, very much not what you expect of a controlled demolition! So why did WTC 7 collapse as it did? For this we turn to the NIST report. This is my own summary of their work.
WTC 7 had a peculiar design. The columns above the Con Ed substation were not directly above the columns around and below it. Reinforced cantilevers between the 5th and 7th floor transfered the load. Trusses scattered around on the 5th and 7th floor stabilized the cantilevers. This seems like a crazy design decision to me but I'm not an engineer. [Update from discussion - the design allowed the building to span a subway station.]
When the South Tower fell WTC 7 took only minor damage. However, when the North Tower fell WTC 7 got clobbered. Debris covered the walkways in front of the building and part of the roof. The SW corner was knocked out from the 8th to the 18th floor. The middle 1/4 of the south face was destroyed beneath the 10th floor with damage going well into the building. There was a hole on the 14th floor where something big went in. 2 elevator cars were knocked into the lobby. Fires were reported on the 6th, 7th, 8th, 9th, 10th, 11th, 12th, 21st, 23rd, and 30th floors plus additional fires in the 20s and 30s not assigned to specific floors.
The south face damage extended right up to the cantilever trusses and there were several diesel generators right there as well. Fires were never demonstrated at the generators proper but the tanks, which were kept full, that supplied them were later found empty with little diesel drained out beneath them. The collapse initiated above the termination of two of the cantilever trusses. Presumably one of the trusses pushed or pulled a support column out of line; that collapsed, taking down the east penthouse, causing the entire building to collapse. The situation is somewhat similar to the Twin Tower collapses: after extensive structural damage and a prolonged fire support structures simply gave way. They differ in that the Twin Towers also had fireproofing damage while WTC also had an unusual structural design placing heavy shearing loads on critical elements.
In summary, WTC 7 did not undergo any kind of controlled demolition. It fell due to failure of a vulnerable and complex trussing system exposed to both major damage and high heat.