Season 0: I haven't finished this yet; I've seen 20/27 episodes. Tristan has more depth, we have another main character (Miho) and it's a lot more dark and gritty compared to Duel Monsters. Although I like the darker and more hopeless atmosphere, the characters still don't really appeal to me.
YuGiOh! Duel Monsters: Classic. Who doesn't love DM? It has so much energy and heart in it, and though it's corny as ******** I can't help but grin along with the characters. I'll always love this series.
YuGiOh! GX: Haven't seen it yet, unfortunately.
YuGiOh! 5D's: Ah, 5D's. Started this two days ago. I'm up to episode 24, and I am loving it. The characters are given time to be introduced (unlike DM where you're just given a ******** at the start) and they have more depth compared to the rest. We have a whole new cast, with likeable characters (Yusei, anyone?) and great music. A unique twist on the game involving D-Wheels makes the duels faster-paced and not as dull, and synchro-summoning is a great touch. I've only seen 24 episodes of this, but I can already say that it's my favourite out of the YuGiOh! franchise.
YuGiOh! Zexal: Haven't seen it yet, too.
So, in my (valid, once GX and Zexal are excluded) opinion:
YuGiOh! 5D's > YuGiOh! Duel Monsters > Yu-Gi-Oh! Season Zero