Tried those leather welding gloves... works for most but not all cacti, unfortunately. In my experience anything leather eventually becomes a pin cushion. I still use leather gloves a lot, but I try and avoid handling cacti directly with them.
Gene, I like the idea of the mesh gloves, but those that I have seen so far all had space in between the mesh large enough for cactus spines, if know of any that don't, please point me in their direction.
For the really big cacti (the large barrels and pole cacti and such) I use pieces of old carpet that I wrap around and then tie down with a bungie cord or two.
The reason I prefer wadded paper over things like plastic bubble wrap or towels is that paper is way easier to tear and remove when it gets stuck on the spines than plastic or cloth in my experience.
Like Gene, I also have a selection of salad tongs and other grabbers that work really well on the smaller cacti and for grabbing onto Prickly Pear and Cholla sections that have fallen or need pruning.
