BAGHDAD — Vice is making a comeback in this city once famous for 1,001 varieties of it.

A liquor store in the Karada neighborhood of Baghdad. The stores were tolerated by Saddam Hussein but shut by militiamen after his ouster in 2003.

Gone, for the most part, are nighttime curfews, religious extremists and prowling kidnappers. So, inevitably, some people are turning to illicit pleasures, or at least slightly dubious ones.

Nightclubs have reopened, and in many of them, prostitutes troll for clients. Liquor stores, once shut down by fundamentalist militiamen, have proliferated; on one block of busy Saddoun Street, there are more than 10 of them.

Abu Nawas Park, previously deserted for fear of suicide bombers seeking vulnerable crowds,...