My vets advised I feed my 3yr old Border Terrier vegetables to bulk out her Chappie meat coz she's always scavenging for food and she's a little porky.
What veg are the best and are they best cooked or raw. I know onions are a no no but are there any others that must not be given to dogs.

I have a "Dog  Veg Stewpot" on the hob and daily add veg trimmings plus add garlic  All my veg trimmings go in this pot, it is boiled up daily  plus I add herbs if I have spare
I also buy cheap veg from shops  to add if I run short as only two in household to feed now kids all gone.
Carrots, spuds, greens all varieties, swede, parsnip, sweet potato, all green beans peas  occasionally add extra frozen spinach  When coooked mash it down and serve it to dogs warm with tripe or whatever meat they having  In winter they have it warm with terrier meal just before bed as an extra as some of mine live out .
  

Vegetables lose a lot of their useful nutrients when cooked (lightly steamed if cooked at all is best)  alternatively, save up suitable veg peelings such as carrots, broccoli stalks, cabbage etc in a bag in the freezer, then blitz it very fine in a food processor/blender.  I add this sort of thing to my dogs' dinners - they are raw fed.  I'm not sure veg is all that important for them - but i like the idea of no waste! :-)

If the idea of the veg is purely to add bulk then it does not matter and many dogs will eat cooked eg far more readily than raw.

If the veg is to control weight then avoid veg root veg as ti is quite calorific.  Frozen green beans, broccoli and cabbage are low cal, and quite cheap if bought frozen.  Raw blitzed or steam cooked is better of course, as for us.

my dogs eat any vegetables. they have about 2-3 large carrots a day. plus anything else going. they love all veg.

My sister said that broccoli is poisonous to dogs but I've never heard that before. I have given it to my dogs. Willow - who is teething has a raw carrot and raw apple most days. She makes an awful mess with the carrot - but it keeps her quiet for 20 mins!

I am a busy dog mum so I either cook extra veg for our evening meal or give them a birds eye steamer to share.  Carrots, green beans, sweetcorn, broccoli, cauliflower are ok but their favourites are peas which they adore!  Raw carrots too.  Veg provide useful vitamins.

sweetcorn, peas, will add calories, the veg is to fill the OP's dog up while cutting it's food down..

Sweetcorn just comes out whole the other end so is undigestible.  My oldie absolutely adores runner beans but during the summer was actually pulling them off the plants in the veg patch.  He's also a devil for plucking tomatoes off their vines and raspberries off the canes!!!!!!!!!!!  He will also do anything for an underripe banana.....if its older he wont touch it!!!  I sometimes add leftover veg from our meal to the dogs dinners and have noticed that my youngster just loves broccoli with fish4dogs trout mousse ontop.........a new take on fish pie??!!