For some veg it makes sense:
- the peelings of well-scrubbed carrots and parsnips,
- the bits you remove if your celery is stringy, and celery leaves (I grow my own so always have leaves)
- non-muddy trimmings of leeks, spring onions and other alliums
- onion skins - but only if you want your stock brown.
- outer leaves of brassicas, but in very limited quantities or the flavour will dominate. Can be better if browned first, and of course must be well-washed.
- If you grow your own veg, the top growth of garlic and carrots can be added, as can undersize leeks and spring onions as you thin them.
- Home grown herbs can be added stems and all, though probably not really woody bits.
Potato peelings only add starch, not flavour, and are best avoided.
In between are things like squashes - they'll add very little flavour, and probably a bit of starch that you probably don't want.
You do need quite a lot. I'm more likely to do this making turkey stock at Christmas when I have the bones to go in as well, and I'm preparing a lot of veg. Even then I usually add an onion or two as well as herbs from the garden.