When looking to buy a used laptop there are certain things that you should know about the laptop.
1. Processor speed- P4 is faster than a P3 laptop
2 There are several types of mobile processor- this guide only covers Intel chips. AMD I know less about.
A. Mobile P4- slower than the others, even with the faster clock speed (128,256 and 512 L2 cache)
B. Centrino- optimised for laptops in either Banias (512->1 gig L2 cache) or Dothan (2 gig L2 cache) can come in 400mhz bus (Dothan) and 533 bus (Sonoma)
C. Intel Core Solo, and Core Duo (code-named Yonah or Core 2 Duo (code-named Merom; for Napa Refresh) processor with a 667 MT/s FSB- Similar to Dothan or Sonoma, but two cores are squeezed into one chip Different Ram speeds.

See the wiki page for more details on the different Intel mobile lines at wikipedia search centrino and intel.

1. DDR2 is the fastest available ram- speeds vary from 533 to 667, to over 1066 MHz
2. DDR ram comes in different speeds (the faster the better) from 266 thru 400 MHz
3. SDRAM is the slowest, and comes in 66mhz, 100mhz and 133 mhz.

Different Hard drives:
1. 4200 Standard laptop slow drive
2. 5400 faster drives
3. 7200 RPM FAST laptop drives (can be noisy, and run hot)

Ide was the standard, but the newer laptops can have the Sata- or serial ATA hard drives. Be aware that they are not intercompatable, and Sata drives may be harder to source at the moment.
When looking for a hard drive for a laptop be aware that the slower the speed, the slower the performance. Drives generally have a 1 year warranty- so buyer beware! Seagate Drives generally have a 5 year warranty, but you need to check the status as OEM drives have no warranty. Ideally a larger cache will give you better performance. Most drives have 2mb of cache, but newer faster drives can have 8 or 16mb. You get what you pay for, and you're lucky if your drive lasts longer than 2 years for laptops!

àupdate- Vista compliant laptops are now REQUIRED to have new hybrid hard drives as of June 07. This is essentially a hard drive with some flash ram for faster performance. So Far only Samsung and Seagate offer these drives strictly for oem’s and they are not yet available to the general public. Solid State drives which are pure flash ram drives with extremely fast performance times and no moving parts are also available, but extremely expensive at the moment.

Screens range from 14.1 inches diagonally to 15-17" and are becoming more popular in wide screen formats. The higher the resolution, the bigger the price tag! You should look for at least a resolution of 1024X768 for a start.
It's crazy- but with the prices these days and rebates you can get a new laptop for 100-200 more than a used one. Shop around and compare prices. Even the best deals may not be that good. If it's a celeron it will be slower, and a 1 year warranty should tell you something about the quality. If there's an extended warranty on a cheap 1 year laptop I suggest getting it. Also- look at the numbers of used or broken laptops for any particular model or brand on E-bay to get an idea of the quality out there. If there are very few of a particular model for parts then they generally are not breaking much. If you see a LOT of a particular model or brand steer clear of them.