If you’re going far away to school (and flying), a lot of the following stuff you can buy at the nearest target or wherever. If you’re driving you might want to start shopping now and you can fill up a car with your stuff. Here’s a list, in no particular order:
Bedding, towels, and such. Your dorm room will probably have a twin-xL bed, so make sure you buy the right size sheets. Buy pillows when you get there if you’re flying, throw some into your car if you’re driving.
A desk lamp, trash can, alarm clock, laundry basket or hamper. Again, all this stuff you probably want to buy when you get there.
Basic food utensils, a plate, bowl, mug, and silverware. Even if you think you’ll be eating in the dining hall all the time, believe me, you’ll want this stuff.
Sticky hooks for hanging stuff (bathrobe, towels, scarves, coats) on your walls. Dorm rooms never seem to have enough hooks.
If you’re going to have a roommate, coordinate bringing a mini-fridge and/or microwave with them. This is something you can probably live without for a few days, so if you don’t know who your roommate is you can hold off until you get there and meet them. It’s definitely very handy to have both a fridge and a microwave, although if there’s a dorm kitchen with a microwave then it becomes much less necessary.
Games! Definitely a pack of cards, any board games you have and like. Party games like Taboo are fun too.
Photos from home. It’s nice to have some printed out to hang on your walls.
Don’t bring a TV! Everyone just watches movies and stuff on their laptops.