I have a pair of lined thick leather gloves that I use in repotting and various cacti duties.
These are the type that are smooth on the outside - not the rough or suede like pairs. These alone do not stop spines, but I use them in combination with "gentle" or "light" handling.
In other words, I will balance the top of a columnar, but hold the bulk of the weight by the roots or between the ribs. Or if I have to pick up spined surfaces, I spread the contact area as much as possible so that there is not much force exerted on any one spine.
Spines still get through, but that's just cactus-grower acupuncture and is good for you anyway.