Sweet, I never thought we'd actually get to keep one of these threads. But I actually want industrial recommendations, just three or four bands to see if I even like the genre.
Most people would say Skinny Puppy... but they're really a horrible choice as they're quite inconsistent with their genre.
SPK (early work, however, for a good demonstration of most of their work and their Industrial stuff, I suggest checking out the "Auto-Da-Fe" release.
Public Works (aka The Tape Beatles) they focus very strongly on samples.
Cabaret Voltaire (I suggest "The Original Sound of Sheffield" which, like "Auto-Da-Fe" is kind of a best of)
Monte Cazazza (while I like his Atom Smashers project better than his solo work, it's quite interesting.)
That should give you a good idea of the range of Industrial music.
you could also check out "The Industrial Records Story 1976 - 1981" for a solid compilation of early Industrial music.
...You should also check out The Grey Wolves to round out the Industrial sound... I could also recommend some Noise and Power Electronics... but they're a bit harsher than plain Industrial.