SO many great ideas and thoughts here.... wish I had seen them a year ago!

DD is just finishing up her first year at University and I agree with so much of what has been shared here!
Amazon Prime is a LIFESAVER at times! Brought DD back to school just yesterday after spring break.... and she realized that she left her phone charger at home. She was able to borrow one from a friend for a few days and I was going to ship hers to her.... but discovered that for just a bit over the price of USPS shipping, I could send her a new one through Amazon Prime! Plus she texted me last night to say that she forgot to buy hair conditioner and could I send some! That would have been an expensive package.... so I added two types of hair conditioner to the Amazon order (one was a great deal since it was an "add-on" item).... and I also added a package of her favorite instant cappuccino mix (a bit more expensive than the local Target, but not always available here). She will get her necessities and an extra surprise day after tomorrow!
DD has been a go-getter about finding the cheapest text book options, but we did end up feeling a bit ripped off from Amazon this year. They refused to take a return on a damaged book (it wasn't any more damaged on the return than it had been when we received it) AND they took so long to return it that even though DD got an offer to buy it, she wasn't able to sell it because it arrived 2 weeks after classes started.

Very frustrating. She will try to sell it again next year. Guess we should have documented the damage better when we received the book and notified Amazon at that time.
I agree with the BUY LESS camp.... dorms always hold less than you think they will and there is no sense in a small room having two of everything. Plus there are RULES... so many more than when I went to school... about curtains and wall hangings and types of fridges/microwaves, etc.
Command adhesive hooks and velcro strips.... you will NEVER have enough!!
If you live close enough to visit after a few weeks, may be leave some things behind until you know if they are really needed. DD ended up needing an additional bookshelf (over and above the one we brought). Her original idea of keeping her books/notebooks on her desk just didn't pan out.... once she put her printer, lamp, pencil cup, and laptop on her desk, there was NO ROOM left for books. But she was able to live without it for about a month and that gave me time to find a used one the right size, paint it, and bring it to her in time for my first "scheduled" visit! And speaking of printers.... we sent DD to school without one because folks had advised us that they aren't used much because so much is submitted online.... and DD can print a certain quantity at the library for free each semester. But all it took was one phone call from DD at nearly 2 am asking me to keep her company while she walked across campus to the library to print something that she needed in the morning, for me to decide to buy her a printer all her own!!
I doubly agree with the Mom who mentioned packing up a medicine kit. Nothing elaborate, but enough to get your child through a 24 hour period of time without having to hit health services or go to the local market..... a bottle of Advil or Tylenol, a package of daytime/nightime cold medicine (Target sells a combo pack), anti-diarrheal meds, Pepto (tablets store easily and with less room), Tums, and a "boo-boo" kit.... multiple sizes of band-aids and bandages, a few gauze pads, alcohol wipes, anti-biotic ointment, and a tweezer and needle for splinter removal. I also included a few of those instant cold packs (the type sports teams usually carry around) and a few of those instant warm wraps (for sore shoulders and such). If they have enough space, a "sick day" kit isn't a bad idea either .... a small bottle or can of ginger-ale, a sleeve of crackers, a box of GOOD tissues, cough drops, Gatorade, a can of soup, tea.
As far as school supplies go.... printer with extra paper and ink (so that they don't have to buy these things at the overpriced school store), calculator (with extra batteries.... ditto the school store thing), pens and pencils, scissors, ruler, a small pack of colored pencils (sometimes they need to do drawings or diagrams, even in the most unlikely classes), tape, binder clips and paper clips, and a stapler. That should be enough unless your student is majoring in something like Art or Architecture, etc that might require something special.
Small lock box/safe.... we bought the smallest one available at Target and it was been just enough.... holds cash, passport, back-up drive for laptop, and the emergency credit card I sent along. She has it locked to a part of her bed frame out of sight (why tempt people?).
Towels and sheets..... DD opted for WHITE for all of this and in the long run it has actually turned out to be a GREAT idea. We can bleach it all if she has been sick or gets a stain and it can ALL to in the washer together.... no need to sort the linens into different loads. Glad she made the more practical choice, since I was leaning toward fun colors!
That's it for now! Best of luck to your children!...................P