Why not? I can't see why the new machine wouldn't be able to read any or all of them, unless you have them formatted in a way that the OS on the new machine doesn't understand - e.g., NTFS drives on a WinME machine.
Unless you mean you want to just stick the drives in the new machine, and boot them and run the software that's already on them. That's a dicey proposition, at best.
Its doable if you clear the Registry (assuming Windoze) of hardware info under HKEY LOCAL MACHINE ENUM.
Clear everything under ENUM before removing the HD from the old system. Place HD in new system and start up. Windoze should detect the new hardware and install drivers accoringly.
Note: The above works for 9x. For W2K the process changes. Basically you'd have to boot from the W2K CD and do a "Repair" of an existing installation. This will detect new hardware and copy appropriate files.
I've done both proceedures over the years without any major problems.