Yes, they do. The last time I went to it was 5 years ago (summer of 2005), but according to Coney Island's official website, the Coney Island Circus Sideshow is still running this year, 2010.
Be warned, though: it's not a particularly exciting freak show. It's definitely nothing like the freak shows in the old days. They only have a couple of performers, and none of them are "real" freaks (you know, like, the bearded lady, Siamese twins, the mermaid lady). None of them are deformed.
Instead, they do tricks. There's one guy who swallows fire and escapes from a straightjacket in 2 minutes. There's a guy who lays on a bed of nails while people jump up and down on him, or put heavy blocks of concrete on him. Then there's a tattooed lady, and this really weird old guy from Brooklyn who acts as an MC (Master of Ceremonies).
It only costs $5, so, it's not like you get ripped off. But it's not like, something you just CAN'T miss.
When I was there, the freak show was located just inside the main entrance to the park, on the right side. But according to the second Related Link (see below) the freak show has moved this year.
Yes, Coney Island is still open for business every summer.
Coney Island Hot Dog Stand was created in 1966.
Coney Island opened on January 1806.
"D" train to Coney Island station.
Coney Island is a landform in Brooklyn.
Coney Island's area is 64 acres.
No Coney Island is in the United States in North America.
James Coney Island was created in 1923.
The ISBN of A Coney Island of the Mind is 0811200418.
A Coney Island of the Mind was created in 1958.
Donna Coney Island is 5' 4".
Coney Island Cyclone was created in 1927.