The machine is not properly resuming since I upgraded to Ubuntu 10.04. Folks seem to have the same issue but it always takes me an hour to get the right fix from the Ubuntu forums. Therfore, my personal entry.
It looks like the new kernels have an issue with old Radeon or ATI graphics cards such as those built into the IBM Thinkpad R50 or R51. However, adding a simple “nomodeset” to /boot/grub/menu.lst does the trick.
title Ubuntu 10.04.1 LTS, kernel 2.6.32-25-generic root (hd0,0)
kernel /boot/vmlinuz-2.6.32-25-generic ... nomodeset
initrd /boot/initrd.img-2.6.32-25-generic quiet