Its hard to keep track these days.
I thought they were on Quake1 and then went to Quake2, but that didn't count because it was jsut experimenting. But then from Quake2 they scrapped it for Unreal (1), scrapped a major portion of the visual methods, code or whatever shortly after the 2001 E3 video as I remember old posts shortly after where George was saying the appearance of characters etc in the game were a lot better than seen in the new E3 video, and a PM I got in response to something I posted in some thread I can't remember from a 3DR employee saying the particle systems were also redone since the E3 video(2), and then I thought George posted something saying that they restarted in 2002. Although this time being more definate given that they've long since finished the rendering portion of the engine as well as most enemies and all weapons (3).
I don't think anything is ever completely scrapped, like they just deleted all art, code or whatever and said "**** it, we're starting over". The closest was probably the Quake2 to Unreal switch.
Then later on I guess the switch from using traditional methods of single textures to normal mapping which tends to require no fake shadows or shine painted into a single color texture, and instead using a normal map with a grayscale specularity channel in an alpha layer, and then a more plain looking color texture which would mean any surface they decided they wanted bumpping on they'd have to redo.
I think each time was just an abortion of their current engine or a major part of the code, as any models and textures can easily be carried over. They have a game model made and textured in whatever program they use, if they switch engines they just need to code a new exporter for their program and they can just export everything to the new engine.
I guess the actual number just depends on how far people want to go to declare it being scrapped. Maybe not totally scrapped but I think there was one instance before starting over in 2002 or whenever it was that they'd canned something before starting over.
I think part of the reason Joe can't post pictures but of a few old people at 3DR is because they probably lose chunks of the team each time they start over. The only people there from beginning to end I think are Ruben and Charlie right?