The essentials include bedding, clothes hangers, an alarm clock, towels, a shower tote and toiletries. Because most dorm mattresses are small and thin, you may also consider an "egg crate" pad to soften up the sleeping surface. Beds are also usually twin size and extra long, so check with your university, and then buy the appropriately sized sheets. It's also a good idea to take a laundry basket or hamper, cleaning supplies (including laundry detergent), and a decent-sized trash can with bags.
Although nearly all colleges now have computer labs for students to use, it is very convenient to have a computer in your dorm room. Computers are personal choices, and you will have to decide what brand and size you prefer. But regardless of whether you choose a laptop or a desktop, you should take an extension cord and a surge-protector equipped power strip, as dorm rooms often have few and inconveniently placed receptacles.
Dorm rooms are personal spaces, and you will want to decorate it to your and your roommate's individual tastes. You may want posters, artwork, area rugs, beads, or pictures from home to decorate this space that will be your home for several months, perhaps even several years. You will need basic tools to hang decorations in your room; a multi-tool is a good thing to take, as it will contain pliers, screwdrivers, and other useful tools all in one package.
Dorm rooms are notoriously small and college students have many belongings. Storage bins will give you the opportunity to pack away winter clothes during the spring, or store items such as shoes or games that you don't need every day, but don't want crowding your small amount of floor or shelf space. Consider buying plastic containers that can fit under the bed or on the floor in the closet.
You may want a television, DVD player, microwave, or refrigerator in your dorm room. Because these are not necessities, and because you definitely don't need more than one per room, you may want to ask your roommate if he or she wants to share this responsibility. Perhaps one of you can bring the television and the other can bring the microwave, for example.