This is a really tough category to nail down. There are a ton of awesome D&D races out there. All things considered though, I think I'd choose the 4E version of the dragonborn.
Dragonborn are non-traditional in D&D (existing only in 3.5 and 4E, with vastly different interpretations in each), but to my mind, they are possibly the most interesting race in D&D. They take after dragons, having tough, armored scales, a breath weapon, and a predilection for the arcane arts.
To me, playing a dragonborn means getting to play a humanoid embodiment of what dragons are all about: six feet of badass scaled spellcasting. It's the next best thing to having an actual dragon character.
Part of why I love the dragonborn so much is that, despite being so new to the game, they are immediately recognizable to newcomers. If a character has a scaled hide and can throw a breath weapon around, that character is immediately compared to dragons. However, despite that, they don't have the kind of history and stereotypes that elves, dwarves, and similar races have, which makes it even easier to give them a unique place in a campaign world.
All in all, I love the dragonborn. They're so much more interesting to me than more traditional races.