Biological Ironies

I was watching David Byrne + Daniel Levitin at The Seed Salon yesterday evening and heard Daniel Levitin (the professor dude) talk about how ironic that the brain, which receives sensory inputs from all over the body, does not itself have sensory nerves. He further added helpfully that you would not know if your brain is poked. It's a nice bit of detail to draw a non-biologist into conversations about biology and brain.

I suppose evolution did not have a good case for the brain to have sensory nerves. It had, after all, already floated the brain in a fluid and surrounded it with a thick skull. There is no value in wiring it with sensory nerves to detect physical harm. I mean, if your brain has been physically poked, you are goner, you are a late person, your metabolic processes are now history, you have ceased to be...

Here's a question along those lines. Is there any other body part (skip the bones, ligaments, etc) that lacks sensory nerves like the brain? Can we, say, poke another organ - apart from the brain - without knowing?