Starchy veg have points - peas, sweetcorn, sweet potatoes and parsnips but as far as I know they are the only veg with points.
I like to have a huge salad for tea in warm weather - iceberg lettuce, spring onions, baby tomatoes, diced sweet pepper - all 0 points. I have a tin of tuna with it (2 points) and waistline salad cream which is 0 points as long as you only have a dessertspoon of it which I find is plenty to mix with my tuna.