Where Will You Take Your Computer?
First of all, will you be carrying this computer everywhere? Meaning, will you take it with you to class every day, to the library, to coffee shops, etc.? If so, then you will need something portable and lightweight. In my opinion, anything over 14.1 inches will be too wide and heavy to carry around. Note that laptops averaging about five pounds are an alright weight. Something like the HP Pavilion DV4-2161NR above has an ideal weight and screen size for college students.
Specs of Computers for College Students
Now that we have taken care of the physical aspects, let us talk about the specs. Ideally, college students write a great deal on their computers. I can't even remember how many papers I have typed up on my laptop, some of which exceeded 20 pages. Thus, having a large amount of hard drive space will keep the computer running smoothly when all those papers are piling up inside. The hard drive is where everything will be stored, essays, music, videos, everything you have will be stored there. Which brings me to another point, back up your hard drive OFTEN! You know, just in case your computer decides to crash right before you print out your essay. I am straying off-topic, but this is crucial. Use a very large memory USB flash drive to save all your important documents, or use an external hard drive. Another option would be to copy and paste your essays to your email often during the writing/revision process and send it to yourself or simply save as draft.
Hard Drive & Internal Memory
Now, going back to the topic of hard drive, you should buy a computer with at least 250 GB of hard drive space. It might seem like a lot, but these days computers with over 500 GB are selling for about 50K. Memory is also important, so something like 3GB or more is a good deal. Remember you can always use external memory cards, or update your internal memory (if you know how to do so) later on. Battery life is another factor to put a lot of consideration into when buying a laptop for college students. When searching you will see that some laptops will say "4-5 hours of battery life" when in reality the battery will only last half of that time. Then again, it all depends on many things: Was the battery fully charged without disturbance? Are you using the battery on a balanced light, instead of on bright light, etc? Some things will kill the battery pretty quickly, so keep that in mind when looking at battery life.
Operating System
You also have to think about the Operating System you want to get. Previously I used to think Windows XP is the best and I still do, but once I tried Vista, I am liking it as well. However, now there is also Windows 10 and that seems to be great. In the end, it all comes down to YOUR preference, so whatever you think is best for you is what you should choose.
Processor
Last, but certainly, not least is the processor. You have to pick a processor that will keep up with you and not slow down any time soon. Something like an Intel Core Duo, Intel Duo Core 2 or above is alright.
I know for college students, computer hunting is not easy, but the above info should help you a bit. Now your next concern is probably when to make the purchase.