The choice isn't if you need a computer in college, it's what kind will be best for you. Some students have laptops; some students have desktops. How can you tell what your best option is?
Laptops

Pros
Can bring it to class and use it for note-taking
Can take it to the library or a study group session
All of your information (notes, papers, research) will be in one place without much effort
Cons
Can be damaged easily if not protected
May not have as much memory as a desktop
Can be distracting in class (IM, anyone?)
Desktops

Pros
May have more power than a laptop
A bigger screen can prevent eye strain (especially if you're looking at it all weekend!)
Less likely to be stolen
Cons
Can't bring it to class
Takes up a lot of space in an already-cramped room
Hard to bring home over the weekend