The story...

Witness accounts of secondary explosions during the WTC collapse strongly suggest there were bombs in the building.

Our take...

Not everyone believes that. Here's an alternative explanation from Civil Engineer Magazine of May 2002:

Once movement begins the entire portion of the building above the area of impact falls in a unit, pushing a cushion of air below it. As this cushion of air is pushed through the impact area, fires burning in that area are fed by new oxygen and are pushed outward, creating the illusion of a secondary explosion.
http://www.pubs.asce.org/ceonline/ceonline02/0502feat.html

This may fit with some accounts, like that of Brian Dixon:

I looked up and you could actually see everything blew out on the one floor. I thought, geez, this looks like an explosion up there, it blew out. Then I guess in some sense of time we looked at it and realized, no, actually it just collapsed. That ís what blew out the windows, not that there was an explosion there but that windows blew out.
http://www.nytimes.com/packages/html/nyregion/20050812_WTC_GRAPHIC/Dixon_Brian.txt

This doesn't prove anything, either way, but it surely can't be ruled out as a possibility. Especially given that no-one observing the collapse had ever seen anything on this scale before, and so had no idea what a bomb-free collapse would look (or sound) like. 

The talk of “multiple explosions” may also have an alternative explanation. Here’s one of the better known accounts.

Veliz went down a staircase with a coworker to the concourse level. In the mall, they got onto an up-escalator as the South Tower collapsed, causing a rush of wind which knocked them down. In the pitch black, Veliz and her coworker followed someone carrying a flashlight:

"The flashlight led us into Borders bookstore, up an escalator and out to Church Street. There were explosions going off everywhere. I was convinced that there were bombs planted all over the place and someone was sitting at a control panel pushing detonator buttons. I was afraid to go down Church Street toward Broadway, but I had to do it. I ended up on Vesey Street. There was another explosion. And another. I didn't know where to run."
http://thememoryhole.org/911/veliz-bombs.htm

This is supposed to support the demolition theory, but then why is this witness describing explosions going off “everywhere”, presumably including nearby streets (as she doesn’t know where to run)? And some time after the South Tower has collapsed? If this was the sound of bombs, then where were they planted?

Perhaps there are other explanations that make more sense. What if gas mains were exploding, for instance? Transformers? The fuel tanks of some of those burned-out vehicles visible in later pictures? We did find one similar account that partially supports this idea.

...we looked up and saw the entire top of the second tower blow up in a 100-foot fireball and debris started falling. The two of us ran back about 20 feet. We then dove headfirst into a doorway cut into the side of a building as debris crashed to the ground. Brian and I were separated and I thought he was dead. I tried to yell his name but couldn't as the smoke and dust were choking me. There was zero visibility. When I finally was able to scream, he immediately screamed back that he was OK. We decided that we had to get out before a secondary collapse trapped us. So, we opened the door and proceeded north, totally blind in the most surreal setting imaginable. There were mini explosions on all sides of us and then a huge gas main blew up, creating a 30-foot torch.
http://origin.web.fordham.edu/Campus_Resources/Public_Affairs/Archives/2001/archive_38.html

So a collapse of one of the towers, then a pause before the witness tries to escape, then reports of more explosives all around, but this time an explanation for at least one. Maybe the others were bombs, but given the fact that the tower had collapsed already, and the explosions were “all around”, we’d suggest they rank low on the list of explanations.