I just finished freshman year and I'd say I had the most unusual experiences of anyone here (unless anyone else goes to Tulane). I had to evacuate my dorm on freshman move-in day because of Katrina and spend my first semester at college at RPI instead of Tulane. So the essentials, some of which I sorely missed at RPI are:
Sleeve/case- I bought an STM sleeve for my Powerbook and its survived many knocks around in my bag. Whatever you choose, try to get something made with high-impact foam if you go for a sleeve, it absorbs/spreads impacts.
A printer- many schools charge for printing, and not having a printer means having to wait for library/dorm lab printers when its exam time and everyone is printing out notes and papers. Coordinate with your roommate on this, you really only need one per room. Having a build in scanner/copier will come in handy when you least expect it.
MS Office- the only time I used this was for Chem Lab every week to print out graphs of my data. Wait on buying the software though until you find out what kind of discounts the school's computer store/software program offers. Also wait on buying other software like Maple/Mathematica/Matlab until you find out what standard on campus- many schools will provide
Flash drive- an easy way to transport files.
Scientific calculator- many Calc I + II classes will only allow a scientific calculator rather than a graphing one; both Chem + Physics I at RPI banned graphing calculators also.
3-Hole punch- good for putting printed notes, old tests and class handouts into binders. Binders mean safely organized and not lost under the bed, in the back of textbooks, etc.
Stapler- good for stapling together lab reports and papers, many times there wasn't on in the classroom.
Pens and mechanical pencils- make sure you like the pens and can write comfortably with them. Mech. pencils write cleaner and are perfect for science and math tests when its inevitiable that mistakes will be made.
Binders and single subject notebooks- binder to keep in your room with handouts, old tests, ect and the single subjects to bring to class and take notes.
Pop-down hamper- try to get one with sturdy handles, as you never know how far the laundry room will be.
Messengers bag/backpack- something sturdy and comfortable to carry around your books and laptop. Go with whatever styles more comfortable.
Desklamp/clip lamp- something to put by your bed so you can work/read in bed (or at your desk) while your roommate sleeps.
Sheets/towels- one set is all that's absolutely necessary, but it's nice to have two so that when one gets rank you can pull out the othher without having to do laundry right away.
As for the computers, only take one. I went back to NOLA in November to retrieve some things (checkbook, IDs, etc.) and also got my Powerbook. RPI had loaned all of the displaced students a T-43 Thinkpad so from the middle of November until the semester ended I used two computers, it was honestly more trouble than it was worth. Back up your files regularly, and leave the TiBook at home in case of tragedy (theft/breakage).
That's what I'd recommend to start with, depending on what your room looks like and your personal habits you can always buy more at school (just avoid the bookstore, usually its overpriced) but especially if you'll be flying to school remember you'll have to pack this all up at the end of the year.