I built a pair of 2x12s years ago and after some doing research it seemed like it was a pretty common practice to put egg crate foam or quilt batting on one of each pair of opposite sides (back, bottom, and one side, say) and then stuff the cab loosely with some sort of poly fill or special acoustic fluff or whatever.
Supposedly this makes the cab "feel" bigger to the speakers, which will give it a deeper and more even frequency response. If you're specifically designing your cabs to be tuned (which I understand most guitar cab builders aren't - the standard classic 4x12 design was apparently just based on trial and error, and trying to get all the speakers to fit into one box) I guess you wouldn't want to mess with foam, because that could make it sound "dead" by flattening out uneven frequency peaks that were supposed to be there.
If you take out the insulation, post your impressions (and some before and after clips)!