Can any cacti be described as fast growing?
Obviously that would be a relative term but I've only really seen the opposite, eg carnegia gigantea being very slow.

Pereskiopsis Spathulata will put on 10cm+ in a week when grown in favourable conditions. Which is warmth and humidity with loads and loads of nutes. The thing is it don't really look like a cacti.

All the grafting stocks grow fast. Trichocereus, Hylocereus, Myrtillocactus, Opuntia, Cereus (most).

There are heaps

it is pretty relative, but if comparing to carnegia there are many "fast" growing species like the ones above.

well as Kada puts it just about everything is faster than a carnegia. except an Aztekium ritteri on its own roots!
what are looking for? columnars? globose? clumping? climbing?
all the grafting stocks stated above are very fast growing under ideal conditions, which is why they are used as stocks for less vigorous cacti.
For globose cacti echinopsis can grow fast and clump like crazy if you pump the hell outa them with water and fertilizer over the growing season. Opuntia subulata can also grow like an absolute weed if given the treatment described above. some pilosocereus sp. can grow pretty quickly to.

I'm not asking for any real reason - other than curiosity. I only have a few cacti of my own at the moment and they seem quite slow in growing.
The only one I can identify is an echinocactus grusonii.
I have bee moving house quite a bit over the last couple of years so they probably haven't been in the best position, probably not fed and watered sufficiently and probably not in the right soil either.

I really like the globes and barrels mostly. I was planning on trying some ferrocactus in spring time.
I guess once I get my garden up and running (in a nely built house) I should ba able to answer my own question

if you want identifications for your other cacti then post some pics under the identification topic and some forumites here will be only to willing to help out