Bedding - You will need bedding supplies for your new college dorm or apartment.
Kitchen supplies - Some dorms allow cooking so you will need kitchen supplies. If you live in an apartment, you will have to cook for yourself and kitchen supplies are a must. Buy some cheap kitchen supplies from ikea which will save you tons of money.
Furniture - You won't need much furniture in the dorm. But in an apartment, you will need a bed, some chairs, a table and other stuff that you think you will need. Talk to your roommates so you won't buy duplicate of everything.
Electronics - you will probably need a tv in the living room. If you have an old one from home, it's probably better to use it here.
School supplies - notebooks, pens, pencils, and a computer. Make a list of what you need and shop for them so you will have an adequate supply in your apartment for school.
High speed internet connection - this is essential because you will need online services to do those research papers both in the dorm and in an apartment.
A bicycle - a bicycle is lot cheaper than a car and can get you from your dorm / apartment to school. If you can afford a car it's even more convenient for you to get around.