When I was first heading off to college I didn't have the slightest idea as to what I should take, here's a list of what I brought, and what I currently need.

If you are going to live in an apartment, either by yourself, or with a room-mate, I recommend these:

microwave (some apartments don't come equipped with these)
the obvious silverware, kitchenware, dishes, glasses, etc. (I found 40 set glasses at K-Mart for $12.99)
Storage ware (You won't have enough money sometimes to just buy food and throw it away, save it)
Cookie sheets, casserole dishes, etc. (I know you may say that you'll never really cook, but you will, go ahead and get these, it will save a trip to Wal-Mart)
Pot holders (sometimes you cook food a little too long)
Draino (your first move-in might pose some problems, that problem might be old food stuck in the drain from the previous tennant)
Bug spray (especially if you live in the South, you'll find you won't be the only thing that's hungry)
Blender (come on, we all like mixed drinks)
Cutlery (you might find enough spare change to buy some steaks)
George Foreman Grill (the best way to cook any meat..and make grilled cheese)
Dish/Cleaning towels (sometimes you'll make a mess that the paper towl can't clean up)
Dish drainer & little water catcher that goes under it (for those w/o dishwashers)
Shelf liner (you never know what's been in the cabinets)

Of course you will need other items, trash can and other stuff like that, but the above items really stick out in my mind.

Futon (instead of a $400 couch, plus it converts into a bed, can't get any better than that)
End tables (you'll find these really important, I found some glass and metal tables at Target for $29.99 each)
Lamps (they're more relaxing than overhead lights)
Entertainment center (I found mine at Target for $119.99, of course the floor, or crates always work too!)
Key holder (useful if you lose your keys a lot, the one I have is also a mirror so you can catch a glimpse as you leave)
Blinds/curtains (you don't want people looking in at you, some apartments come with blinds, but not curtains, I bought some a K-Mart for $12.99)
Clock (I didn't think I would really need one, yeah stupid, but it is very useful)

I don't have any rugs or coffee tables, I don't really see the need for it, plus I have low funds, but they are nice things to have.

All of my bedroom stuff I brought from home. However, I didn't bring everything because I knew I wouldn't have room. If your parents kept your old bed (twin or something) from when you were little, ask them to set it up for you for when you visit home. That's what my mom did, and it beats sleeping on the floor or couch.

Computer desk/Computer
Blinds/curtains (same thing I said about the living room)

I brought my bookshelf to hold items that are sentimental to me. I didn't leave everything, I just brought items I knew I would miss, such as pictures, words of wisdom, stuffed animals, and other memoribilia. Also, don't bring every single piece of clothing you own. You will find you won't have a lot of room to keep it. I left all of my winter clothes at home, and when it starts to get cold, I'm bringing my summer clothes back, and taking my winter ones with me. It will save space.

Bath mat
Shower curtain & rod (most apartments don't come with one, plus, who wants to use someone else's curtain?)
Towels (bring some from home, or hit a sale at Wal-Mart)
Bath essentials (toothpaste, etc., all the logical stuff you'll need)
Bring toilet paper when you move in! (you will regret it after 5 hours of driving and you need some TP)
Cleaners (please clean the toilet before you use it for the first time)
Laundry basket (mommy won't be doing it now!)

Erasable Calender & white board (use the calender to write down important dates such as an exam, when bills are due, or important appointments. I use to white board to write down phone numbers. It's better than keeping all of the numbers in five different areas scattered around)
Air freshner (buy an air freshner, all apartments have a smell, and I know you won't like it)

Before you move, write down every serial number on every electronic you own, that way, if your apartment gets robbed, you have a better chance to recovering your items.

If your car does not have a security device, have one installed. Many cars on and off of campus have been stolen or broken into. I'm sure you would rather be safe than sorry.