A bit of background: I have never lived on campus. Once I left my apartments, whatever I had on me or in my backpack is what I had to deal with the day. This made me learn what I really needed on my person for my daily activities, and what just weighed me down.
Here are some useful items to carry with you that will ensure that you'll be ready for anything!
Weather permitting items
This is anything from wearing shorts to bringing an umbrella. I always check the weather before I leave my apartment in the morning. You might get caught in an afternoon rainstorm and get totally drenched while walking home. I have done this too many times. I would just grab an inexpensive umbrella from your local store.
A good pair of shoes
There is a fun game for older students to pick out the freshman walking around campus. One of the biggest faults that reeks of inexperience is wearing heels to campus. If your campus is moderately large, you will be walking a lot- like miles a day a lot. Unless you have a reason to wear uncomfortable shoes, wear something that you can walk for a while in. I prefer a good pair of tennis shoes.
School supplies
Self explanatory- bring what you need to take notes or do homework. Anything from a laptop to a notebook. Just remember to bring what you need. I also like to keep my planner and a set of pens in my backpack just to keep on-track with what I need to do.
Medications
Bring any perception medications you need during the day. Also grab your favorite brand of pain meds for those rogue headaches that come out of nowhere. It happens and it's better to have them than not.
Travel coffee mug
If you drink coffee, its nice to just refill your cup when you go through it. Plus, many places will give a discount for using your own mug.
Water bottle
I prefer one with a filter because you can refill from anywhere and be okay. When you are walking around in the heat, this is a life saver.
Chargers
Phone charger, laptop charger, etc. It's nice to have them and not use them. It's better than having your laptop die half way through the day.
Wallet and student ID
You will need your ID at some point, if you college uses them as a way to pay for food, or to check out supplies at the library. It is nice to always keep them on you. I use a phone wallet so then I don't need to carry a separate wallet.
Personal stuff
Extra female supplies, makeup wipes, hand sanitizer, chapstick; pretty much anything can be added here. Some people will have a small pencil bag to put all of these items it in. I just put them in the compartments already sewn into my backpack.
Fun items
When I was at Junior College I'd keep a deck of cards on me because I would have friends who would play games with during lunch time, or a personal book to read during breaks. My main thing is that if I use my laptop for entertainment during a break, I won't get back to what I need to work on later. Therefore, I would bring other things to keep me occupied without getting me off track. I would also include headphones here, you don't need the latest model of the fanciest headphones here. Just something to give you some music while walking or studying will make your day.