you don't have to bring a printer, but it's soooo much easier to have one in your room. my college gives me $20 worth of free printing on their papers and I only used it for really big printouts. smaller stuff, every day stuff, i used my own printer. it's so much easier to have one in your room than having to find a printer to print out your term paper at 3 am, especially if there isn't a computer cluster in your dorm.

in my big lecture classes, most people used laptops, but my smaller classes didn't at all. it really depends on the class, and what you're comfortable with. i used my computer in some classes, and notebooks in others. i will say it's easier to keep notes organized if they're on a computer.