Spring is a great time to plant berries and fruit trees. Most Fruits and berries will perform best planted in full sun, a few prefer some shade.
Melons - Watermelon, Cantaloupe, Tiger Melons and some of the more exotic melons can be started in many zones in the early spring. In Northern regions with shorter growing season they can be started indoors to get a head start. Northern Gardeners are advised to see - Short Season Melons.
Berries - such as Raspberry, Blueberry and Strawberry can be planted in the early spring, although requirements vary from cultivare to cultivar.
Blueberries - A blueberry plant will take 3-5 years to get established and bear good yields, so don't expect to be harvesting much - if any the same season you plant them.
Strawberries - Strawberry plants should be planted in the early spring as soon as the soil is workable. Starting from seed is not advisable when starting them outdoors.
Raspberries - Raspberry Transplants should also be set in the garden in early spring as soon as the soil can be worked.
Goji Berries - Goji Berry is another plant that should not be started outdoors from seed - transplants are best. Transplants can be placed outdoors in the spring when temperatures climb above 50 degrees. It is a perennial, so plants you've set in previously will come out of hibernation and begin a new season.
Goose Berries - Gooseberry plants are best set out in Autumn with bare-root plants. However, they can also be set out early spring as saplings, using a generous layer of organic mulch. Wait till after the last frost when temperatures are consistently over 50 F.
Honey Berry is a little known berry that can started from either bare root stock or transplants in the early spring. Also known as Blue-Berried Honeysuckle, it begins producing by its second season, but not prolifically till its 3rd to 4th season. It's life expectancy is 25 - 30 years.
Some other exotic and unusual berries can be researched at A-Z List Edible Berries
Peaches - Early spring is the best time to plant Peach Trees. Avoid low lying areas and gullies where cold air settles, that's also where excess water from rain run off accumulates. Frost will also settle in these low lying areas much more readily.
Cherries - all varieties are best planted in the spring from saplings - bare root stock. Keep that guy George away- I hear he likes to chop down cherry trees.
Other Fruit Trees such as Apples, Pears, Plums and Persimmons can all be transplanted in the Spring. Even Nut Trees such as Almonds, walnuts, hazelnuts - that's assuming you live in a suitable region. Common Sense also dictates you wait till after the last spring frost.