The smallest system you can run Linux on is a 386 with a floppy drive. The smallest I'm currently running it on is a 386 SLC/25 with 8Mb of core and a 420Mb disk. You don't need FPU emulation just because it's a 386 - only if it's not got a floating point copro (i.e. you don't need emulation if you have a 386DX chip, or a 387 installed on the motherboard).
The smallest system you should reasonably consider running Linux without X on is probably a 486DX with a few hundred megs of disk and at least 8Mb of core, depending on what you want to do with it. If you want to use X at all, a minimum of 16Mb of core and probably a 486DX2/66 (with a faster chip and more core highly recommended) would be sensible. If you're thinking of KDE or GNOME, at /least/ 32Mb of core and a little pentium chip. KDE is reasonably responsive on my P75 with 24Mb of core; GNOME is a little heavier though.
Any MMX pentium with 32Mb or more core will run Linux with X and KDE or GNOME quite nicely.
Oh, and the main problem with Linux on laptops is lack of support for their hardware; they often have funny network, video and sound hardware, among other things. Check the information about Linux hardware support to see if it supports your laptop's gubbins before you install.
- Freon
