Slackware is the most bare-bones Linux distro that I know of. Not for the faint of heart though. You have to install most everything above and beyond the base system by hand (it doesn't use rpm / apt / yum / etc, it's a custom package system that doesn't figure out dependencies automatically).
It also doesn't use System V init scripts (which would cause the VMware install script to fail, you would end up having to place the scripts manually since Slackware uses a BSD style init system)
So I wouldn't recommend this if you want to use VMware.
However, if all you're looking to do is run VMware on the system, you could get a copy of VMware ESX Server. (It runs directly on the bare metal, no OS needed to be installed).
A similar program is that of the Xen hypervisor. It's a lot faster but (in most cases) OSes have to be recompiled to run specifically on Xen (so this means Windows will not run on Xen, unless the processor has VT support -- older / most low-end consumer CPUs do not have this). It does install a barebones linux distribution (in fact they use a modified Linux kernel for the core of Xen).
