As a former poor university student (former applies to both adjectives), I needed a laptop to take notes on.
But my situation is not typical. I am left-handed and have a form of disability that makes taking handwritten notes all but impossible. However, at a young age, I learned to type very fast. Therefore, if I could only have a laptop to type notes on, I could have been happy.
So I went on eBay in June 2003, and I bought a Compaq Armada (Pentium II 400, 64 MB Ram, 4 Gb hard drive), and I got 128 MB of RAM for it. The laptop cost me 225, a new battery cost me $40, and the Ram ran me about $75. All told, I spent much less than $400. What i got was a laptop that ran (and still runs) Windows 2000, Office 2000, and even Dev C++. The thing weighed about 8 lbs and lasted 2 hours on a charge. It was perfect for me.
I sold it in December 2004 for $200 on ebay.
Back in January 2004, I helped an elderly lady purchase a laptop that replaced her Dell Dimension desktop and her Inspiron 4000 laptop. She sold the Inspiron to me for the equivalent of $300 in work. It was a 750-Mhz Pentium IIIm, with 128 MB of Ram and a new battery. Its battery lasted 2.5 hours and it ran Windows XP, Office 2003, Visual Studio 2003, and more.
I sold it in December 2004 for $500 on ebay with a wireless router, wireless network card, all the original software, packaging, and accessories, plus a license for Windows XP Professional.
In the end of November 2004 I bought a Dell Inspiron 8600 new from the Dell Refurbished site. They were running some amazing deals for Thanksgiving Weekend, and I got it for $899. It has a 1.5 GHz Pentium M Dothan with 512 MB Ram, a CDRW, and a 30 GB Hard Drive (not to mention a 15.4" beautiful widescreen).
If you're in the same boat as me, I would recommend one of two things.
1. A dell inspiron 4000. These are good, solid computers from 2002-2003, Pentium III-M processors between 600Mhz and 1 Ghz, and this is a good specimen. They sell for pretty cheap on Ebay. Count on buying a new battery for it though.
2. Dell Refurbished. Depending on their weekly sales, you can find some low-end but brand new (read: better performance and more ram than a Pentium III) laptop for about $500 before tax and shipping. You'll be looking at entry-level models like the Inspiron 1000, 1200, and 2200, but those are good systems.
I could not be happier with my two Dell Refurb purchases.