Jax is the original best duelist ever. He still reigns supreme, being the only one to beat you to death with a street appliance instead of the usual sword, spear or crossbow. In seriousness, he's solid and snowballs hard.
Malzahar's the best mage duelist that isn't an anti-mage or assassin. The highest potential burst damage among mages (yes, it's over 5 seconds but he has long enough cooldowns to call it burst).
Vayne is the best duelist among carries. Her single-target DPS rivals Jax when she's built up, and she's one of the more recent champions to have a steroid that lasts longer than 10 seconds.