I've looked at a number of recipes for vegetable stock. Onions, carrots, celery, bay leaf, peppercorns and garlic are common ingredients. (Personally, I'd leave out the garlic, of course.)

There seems to be a difference of opinion as to whether or not a vegetable stock should include tomatoes. When I was researching recipes for Minestrone, some of which called for vegetable stock and others for chicken stock, if the stock didn't have tomatoes in it, the recipe often called for adding them.

The CIA's textbook for cooks says to use NON-STARCHY vegetables for stock. Mushrooms, leeks, parsnips, parsley and turnips can all be added to the list given earlier.

Older editions of the Joy of Cooking recommended using the tops and peels from non-starchy vegetables to make stock, and also suggested saving the water from boiling vegetables as well as cereals.

Escoffier doesn't give a recipe for vegetable stock, he does give one for court bouillon, which is used for poaching fish. His recipe for court bouillon includes vinegar or wine that has been boiled.

Potato water is sometimes used as a thickening agent.