It is possibly to build a customized laptop. Many PC component distributors sell what are termed 'white box' laptops. These are unbranded laptops made by the same companies that make Dell, Toshiba, HP/Compaq, etc. The plastics might be changed, colors, buttons, but under the hood they are the same. ASUS is one name that makes these systems. These systems are bare bones configuration - no HD, CPU or memory. Typically the battery, optical drive and power supply are included. There are desknotes as well, as laptop form factor with no battery - avoid these. Prices on these bare bones systems range from about $500-$1000. Then you have to add the CPU, memory, etc. Price as always varies based on LCD size, chipset, processor supported and optical device chosen. These can be a good deal if you are looking at the $1500+ range. A white box will save you about $200 or so (rough calculation). On the lower end, a white box solution will actually end up costing you the same or more than a cheap Dell, HP, etc.
On the low end, some cheap laptops from the likes of Dell can be souped up. A Dell 1100 (cheap, but heavy and not great battery life) can be upgraded on the processor, harddrive, optical and memory - hey I've seen this list before. I just replaced my 1100, but was looking at going from a Celeron to P4.
As always, it's best to shop around and do your homework before buying.