The line that comes out as No. 1 in quite a lot of listings is quite an old one, from the 1989 Batman movie; 'You ever danced with the Devil by the pale moonlight?' This line is uttered by both Batman and the Joker at different times (the Joker claims that he always asks this question of his 'prey'), and it's become famous in its own right. For instance, there is a later Star Trek episode named after it ('In the Pale Moonlight'). Previously this was the title of a song, so the Batman line is probably also easier to remember because of that.

However, there are plenty of memorable lines - you can find a list of 25 favourites here, and if you type 'batman most famous line' in a search engine you can find plenty more. Though I see my own favourite 'Quick, Robin! Pass the shark-repellent bat spray' from the 1960s film isn't on any of them!