The current 2.0.x Linux Kernels will still run on 386 based Intel PCs, as well as all the subsequent CPUs of the 80x86 family from Intel. There are current, functioning ports of the kernel to Sparc and Alpha machines as well as the m68k port to the Atari and Amiga machines. With a proprietary micro-kernel there is even an m68k version for the MacIntosh machines. A wide range of SCSI, IDE, and special CD-ROM drivers are available with the ``stock'' kernel. As the kernel is the heart of a Linux system, it is also the fundamental infrastructure of any distribution. Debian is no different in this matter, and many times the flaws in the distribution can be traced back to flaws in the kernel being used.
Debian became a full ELF compliant system with the release of 1.1 and it has not changed the basic library infrastructure since then. There are a wide range of available kernels that will work. When the stock kernel does not work with the hardware configuration of the target machine, it becomes necessary to rebuild the kernel with a new configuration that better suits the hardware situation. When this can't be done with the current kernel, it is sometimes even useful to move to a newer, or older, version of the kernel. A standard Debian system (all packages with priority of Standard and higher) will have all of the development tools needed to perform the construction and installation of a custom compiled kernel.
The less memory the machine has, the more difficult it will be to compile a kernel. With as little as 8MB of memory, it is necessary to have at least a 20MB swap partition/file, but more memory will always improve this situation. Any error complaining about the exhaustion of virtual memory can be fixed by increasing the size of the swap-space.
Note: swap-space - All machines have a finite amount of Random Access Memory. Without a method for dealing with this limited memory the system would crash whenever available memory is exhausted. To resolve this issue, the kernel ``swaps'' memory to disk when not in use, to free memory for use by other processes. This requires a disk partition, or a file, that has been specially formatted to deal with memory swapping.