A laptop is more or less a regular PC as far as Linux is concerned. Things that may not be common on desktops, but are common on laptops, are ACPI, PCMCIA ("PC cards") and power management. Other than that it's basically the same.
I have had a semi-broken Dell Latitude CPi 300 with 128MB working as a server for quite some time and it does well. Plus thanks to its battery it basically has a built-in UPS.