Walletpop.com has compiled a list (using FBI crime stats) of the "25 Most Dangerous Neighborhoods" in America. Two of them are in Memphis: The area around Bellevue and Lamar and the area around Warford St. and Mount Olive Rd. See the complete list, with helpful maps, here.
As with most of these proliferating national "best" and "worst" lists, readers need to be aware that they are created primarily to draw readers and web traffic. But still, it's not a bad idea to know when (and where, at least, statistically) you're increasing your odds of running into trouble.