There's an awful lot of misinformation in this thread.
pxl8 is spot on. Focal length is focal length is focal length. Lenses do not change their focal length depending on what body they're attached to. So a 19-35 goes wider than a 24-105, because 19 is less than 24. It's as simple as that.
What does change is the field of view. As
pxl8 says, using a crop sensor is like looking out through a window; you don't see the whole scene.
Time to post my visualisation again, I think. The left hand image simulates the view through a conventional lens that will fit 35mm film cameras and "full frame" digitals like the Canon 5D. Canon EF lenses are like this. The right hand image simulates the same view through a "designed for digital" lens
with the same focal length. Canon EF-S lenses are like this.
I would suggest that the
only relevance of the "crop factor" is when you're trying to compare lenses on different camera bodies. So for example, I used to have a 28-80mm lens on my old film SLR. Dividing both these number buy 1.6 tells me that a lens on my 350D (1.6x crop factor) that has the same field of view would be 17-50mm. But if you never shot film, or if you don't aspire to owning a full-frame camera, then you really don't need to worry about this.