I had a process in a "uninterruptible sleep" state. Trying to kill it is, unsurprisingly, unhelpful. All the literature on the subject will say that it cannot be killed, and they're right. It's called "uninterruptible" for a reason. An uninterruptable process is in a system call that cannot be interrupted by a signal (such as a SIGKILL, SIGTERM etc).
These typically arise when the kernel needs to do something that could take "a while", and that certainly was the case in this particular situation (a user filled a disk partition and NFS lost its head, but that's for another post). Uniterruptible sleeps are actually very useful; they're needed when a process reads/writes to disk for example.