Eggplants are also called aubergines. They are great in stir-fries, in stews with zucchini and tomatoes, or directly from the oven in pasta's.
Carrots are great as a snack, or to dip in humus. You can also add them to stir fries to add some bite. Don't overcook carrots, or they will lose their taste.
Mushrooms are great as an appetizer when fried with garlic. You can put them in almost any stir fry. To clean, you can just brush the dirt away.
Radishes are great as a snack, or to spice up salads and sandwiches.
Tomatoes are great in salads, on sandwiches, in stir fries. Or eat them as an apple (then take care not to spill tomato juice on your shirt)
Cucumbers are great in cold dishes, on sandwiches together with tomatoes, in salads, or blend them for a refreshing drink.
Red peppers are great as a snack or in stews with eggplant and zucchini. Just remove the stem and white insides (althought those are edible as well).
Leeks are great in stir fry with tomatoes and eggplant, or fry them untill soft and then blend them to a great sause with some olive oil and spices to taste. You can eat both the white stem and green leaves.