I don't know his exact body count, but Bats regularly killed people during the Golden Age. His very first appearance ended with a criminal dropped into a vat of acid, IIRC. He's also snapped a bad guy's neck and hung another one from his Bat Plane.
If you read the Batman comics for any length of time it becomes obvious that Batman wants to kill. But he cannot allow himself that pleasure, or he will lose the moral high ground.
The true reasons behind the No Kills rule are:
A)If Batman kills the Joker, Bane, Penguin etc, then the Writers will constantly have to keep thinking up new Villains for him to fight. Also, the hard core Fan Boys would probably suicide bomb DC head office if you killed off the Joker permanently.:icon_twis
B)The Dark Knight is one of the most iconic characters in the history of fiction. He's a licence to print money. So DC need to keep his appeal as broad as possible, and make him as big a part of the DC Universe as they can.
Batman doesn't get his Hannibal on because you can't have a Serial Killer fighting alongside the JLA.
The only Tier 1 Superhero with a high body count is Wolverine. And although they are both Anti-Heroes, Bruce and Logan are very different characters, in very different fictional universes. Marvel have always been slightly darker than DC.