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
Its hard to pick between Season 0 and Duel Monsters. Both offer the best of what the original Yugioh manga had depicted. Season 0 features lots of games, which keeps it interesting, while Duel Monsters focuses on just one game but I like the story of the pharaoh (plus theres more bakura ^-^)
The original's a legacy. I refuse to let my children grow up without a deck or having watched everything.
5D's is also a legacy. It was...the last 20...ohmygod. I was in tears at so many parts. *SPOILER ALERT;
-Rua/Leo's sacrifice for hi sister T^T [but he comes back good good]
-Yusei's determination during the duel with Z-ONE
-Yusei and Jack's final duel.
I enjoyed season 0 and it's probably my favorite, but when I'm asked this question, season 0 wasn't normally an option so I'll have to pick "YuGiOh! Duel Monsters."
As for the spin off series, I have watched all of them and my favorite is Zexal. Super saiyan in yugioh and playing a card game in space was an instant anime turn off for me, but I decided to give it a chance on release date and I loved it! The first couple of episodes are slow, but interesting enough to get you excited for the next episode. I think that zexal is the only spinoff that actually relates to the original series, if you watched it you can see that most main characters are based off the characters in the original yugioh (imo). I can say when I watched gx and 5ds , my first thoughts were "This is horrible." but of course, being the fanboy that I am, I had to watch til the end.
To me I like Yugioh season 0 and DM because it is so unquie and interesting. I kinda don''t like Gx but I will admit it had its moment. I haven't sat down and watch the 5'ds for here I didn't like the idea of card games on motorcycles. The zexal I don't like because it is a spin off of the original and nothing can out do the original.
How i got into the series is funny. Saw blue eyes for hte very first time. Didn't like ghost kaiba wanted yugi to win. Saw real kaiba being james bond and I'm like yes sercet agent man ^^ before I knew he is a wealthy CEO that spends to much time with his toys.