I am wondering what the correct order in which to watch the Yu-Gi-Oh! seasons is.
As Peter Raeves points out in the comments, a useful listing is available at Wikipedia's List of Yu-Gi-Oh! episodes article. In brief:
- Watch Yu-Gi-Oh! Duel Monsters (the first series, not the "zeroth" series), which is 224 episodes / 5 seasons in length. At any point after episode 144, you can, if you'd like, watch the Pyramid of Light movie.
- If you'd like, watch Capsule Monsters, which is 12 episodes in length. This mini-series was created exclusively for US release (so I guess it's "non-canon" if you care about that), but it's pretty enjoyable nonetheless. It is best to watch it after episode 198 of Duel Monsters as it takes places between 198 and 199. Also since this comment was written another Yu-Gi-Oh! movie Dark Side of Dimensions has been released which takes place 6 months after the end of Duel Monsters. So be sure to watch that before starting GX.
- Watch Yu-Gi-Oh! GX, which is 180 episodes / 4 seasons in length. Note that you'll have to hunt for subtitled episodes if you want to watch the fourth (and final) season of GX - it was never dubbed.
- Watch Yu-Gi-Oh! 5D's, which is 154 episodes / 5 seasons in length. At any point after episode 86, you can, if you'd like, watch the Bonds Beyond Time movie. Note that large segment of seasons 4 and 5 were never dubbed. Again, you'll have to hunt for subtitled episodes if you want to watch these in their entirety. There is also a special ("Shinka suru Kettou! Stardust VS Red Demons") that was never dubbed.
- Watch Yu-Gi-Oh! ZEXAL (series 1), which is 73 episodes / 3 seasons in length. There is also a special (the one featuring Kouhei Uchimura) that was never dubbed.
- Watch Yu-Gi-Oh! ZEXAL (series 2), which is 73 episodes / 3 seasons in length. Since this series only just ended in Japan (Mar 2014), dubbing is still in progress. As of this writing (13 Jun 2014), it looks like the first 40 episodes have been dubbed, with more coming out at a rate of one per week. Once you've caught up with this, you'll be up-to-date with the dubs.
- If you don't mind watching subs, start watching Yu-Gi-Oh! Arc-V, which is ongoing as of Apr 2014. Konami has licensed it for dubbing, but the dubs presumably won't start until the dubs for ZEXAL series 2 are complete.
I didn't mention the "zeroth" series (the one released in 1998) anywhere in there because it's sort of orthogonal to the rest of the Yu-Gi-Oh! anime franchise. As such, you can watch it at any point, though I would recommend watching it just before or after you watch the first series (just to see the contrasting ways in which the two series evolved). The "zeroth" series is 27 episodes in length, and was never dubbed, so you'll have to hunt down subtitles. Note also that a short film (titled just "Yu-Gi-Oh!") was produced, which you might want to watch after you've finished the "zeroth" series.
As the answer above me stated, watch it in that order, but there is also Yu-Gi-Oh! Season 0 (or just Yu-Gi-Oh in Japan) that to my knowledge wasn't released outside of Japan. The show is less yu-gi-oh than the rest, with the very few duels, but it's kinda a prequel to the first season, Duel Monsters.