For me a legend has to be someone that people still talk about years after their peak, so a lot (Edit - think I should have said some!) of the options on here are non-starters for me as they haven't passed the time test.
So, I've gone for Steve Davis ... only just qualifies time-wise from my perspective, but he's the player non-fans mention to me the moment I say I like snooker.
Joe Davis - well, would there really still be snooker without him, pushed the boundaries and the only player to absolutely dominate a generation, eventually when he competed every other player had a handicap advantage against him.
Really got stuck on 3rd player, Walter Donaldson was tempting, as was John Pullman but for me they're behind two others, I've gone for Ray Reardon both from the public familiarity and in the way his play linked eras, but very close between him and Alex Higgins (Higgins takes the public bit, Reardon though is a better link between eras, the number of World Championships Reardon won swung it for me).