You can grow just about anything you want in window boxes. However because it's so sunny you will need to take care as to what plants you need to grow.
Visit your local nursery explain you need plants for window boxes that are in full sun. They will help you choose the correct plants.
As Gina said water, water, water this is the key to having beautiful window boxes. Because the plants are in a small amount to soil, between the sun and the summer heat the soil will dry out quickly. There may be spells when you need to water them twice a day. Also window boxes need to be fertilized regularly.