Check with the Dorm Admin., and if they permit it, get a microwave AND a hot plate burner. Have one skillet, 1 small and 1 medium sized pot (with lids) for cooking. That's all you need for food preparation. Enough dinnerware for at least 2 people with the cutlery. A cutting board, sharp paring knives and large stirring/serving spoons (only 2 or 3). That will take care of your eating. Oh, and a metal steamer fan to go into the bottom of a pot for steaming veggies, etc. You will be amazed how much you can cook with just this minimum cookware. If your careful, you can eat very healthy. Plastic containers to store in fridge are essential also.
Take hand towels to dry off after showering instead of big bath towels. They do the same job but are smaller to store and to wash. To this day, I still use hand towels to dry off after showering. However, take many wash clothes (for body washing, and others for cleaning). Put all your soap, shampoo, deodorant, toothpaste, etc. in a plastic case all together. That way when you go to shower, you have everything all together in one case. Just grab it and go.
Get a hanging laundry bag with a draw string at the top (don't buy a cheap one as you will be glad you bought a good one that will last). Easy for carrying to the laundromat. Buy soap and bleach in smaller sizes. It's more economical to buy in big bulk, but you will have no place to store it, and it's no fun trying to lug it back and forth to the laundromat on laundry day. Dishwashing soap will work (3 small squirts) for a load of laundry if your out of regular laundry soap. I used it (smaller bottles with a small bleach fit just right in the top of the drawstring laundry sack). That way, your only carrying one thing and not trying to juggle 3 or 4 at a time on laundry day.
Only take 1 or 2 dressy outfits for special occasions. Make sure they are acceptable for ALL season wear. That frees up space for your regular clothes that you wear daily. Get a plastic shoe holder that goes over a door. Saves space and lets you store about 12 pairs of shoes.
Make sure your bedding is not the over fluffy kind. Get a thin quilt to go on top and a good fleece blanket to go underneath that with your top and bottom sheets for the warmer months. In the Winter, a good electric blanket will eliminate the need for more bulky blankets. You MUST get a good mattress pad to go on the mattress. You have no idea what or who has been sleeping in the bed prior. A twin mattress pad (even a thick one) is easily washed in a regular loading machine.
Splurge the extra bucks and get a really good backpack. You'll be glad you did in the long run. L.L. Bean has good ones as well as Lands End. they have pockets for your laptop, notebooks, books, pens, etc. Everything organized. Keep everything as organized as possible and keep everything in it's place at all times. Believe me, you will make your life so much easier while in college. Splurge on a couple pair of the most comfortable sneakers or loafers (with extra support) for walking around campus. Your feet will thank you in the long run.
Essential: A good alarm clock (not digital) it will still keep time in a power outage, good reading/study light, fan (desk or clip on), flashlight, hammer, screwdriver that has flat and phillips head (changes). This sounds weird, but you will be surprised how often you will use these tools, and how often everyone will want to borrow them from you. A book light that snaps on your book would be good to have also. Tape recorder as was stated above.
College years are fun. If you prepare beforehand, the rest will come easy.