Nothing unusual will happen if you eat brains. Brain is actually one of the most nutritionally-dense organs found in any animal. From a nutritional standpoint, the brain is the best source of healthy oils in all land animals. It has been reported that human children who grow up eating the brains of animals have healthier brains and nervous systems than those who didn't -- but this isn't because they're absorbing neurons or ganglion juice, it's because a very nutritious diet is beneficial overall.
Unfortunately, the brain is also an organ that can carry a concentrated amount of disease. Mad cow disease, as we all know by now, refers to the degenerative and fatal condition that occurs in cows, which essentially creates holes in an infected cow's brain. Cattle can become infected with the disease by eating feed that contains infected tissue. You think of cows eating grass, but most cows we eat at the dinner table are fed grain fortified with finely ground-up meat for protein. The chickens that were ground up as protein for the cows were probably themselves fed grain fortified with ground-up cow, and so on. If disease enters this feed-and-be-fed-to system, it's suddenly everywhere.
Regulations are now in place to control practices, but it's not 100% effective. If you do choose to eat brains, make sure you select it from a safe source. Make sure it is cooked well. And when you sit down to try it, make sure to roll your eyes around, drool, and moan, "BrrrrraaAAaaaaaains!" before you dig in. It's a requirement.