Should fruit and vegetables be counted in a calorie reduced diet?

Agree w Dr. F. I suspect the question arose because weight watchers changed its plan last year to make most fruits and veggies 0 points. Their aim was to get you eating more of these foods, which will fill you up, and tend to be much less calorie dense than less healthy choices. You still need to reduce total calorie intake to lose weight, and zero points does not mean zero calories.
Yes. Anything you ingest has some calorie value (including water=zero calories). Many fruits are high in fructose (sugar) and many vegatables are calorie dense with a variety of carbs, some fat & protein. Fruits and vegies tend to be less calorie dense than most meats but all must be considered if you want to be successful.
Starchier veggies. Bigger picture: more calories in dairy, meat, starches than in your friendly neighborhood fruits and veggies. So focus on healthy portions of those groups first. But if you're really counting calories, then some fruits and veggies are starchier and have more calories like peas, parsnips, winter squash for instance. Link to easy grouping in comments.
I would add..... I would add that i've known several people who gained weight using this new weight watchers plan. Their total caloric intake increased as they gleefully ate piles of apples and oranges. I suspect weight watchers will eventually realize how silly this change was.