MSG got a bad rap when a scientist coined the term "Chinese Restaurant Syndrome" in a letter to The New England Journal of Medicine. Robert Ho Man Kwok experienced heart palpitations, weakness, and strange sensations of numbness after eating large amounts of Chinese food, and his colleagues decided that MSG must be the culprit. Today, many restaurants label their food as "No MSG" to appease the individuals who claim to experience these symptoms when they consume the compound.
Here's the thing: Natural glutamate occurs in many foods, and is used as an additive in tons of "MSG-free" products. And don't even get me started on the "umami" craze - anything that claims to have umami flavor is probably using natural glutamate, and tons of it. But because of the chemical similarity to MSG, there's no reason why eating a fancy umami burger should be any better for the MSG-sensitive crowd than eating a bowl of fried rice.
It's true that an early study found that mice suffered ill effects when researchers injected MSG into their brains, but these results fall under the heading of "there's such a thing as too much of a good thing, especially when you inject it into a mouse's brain." Human studies have failed to produce significant symptoms, even in those who claim to suffer. Scientists report that mild symptoms can occur in some individuals, but only if they consume large amounts of MSG on an empty stomach. If you avoid scarfing down cup noodles when you're starving, you should be just fine.