I started playing in mid-2012 (HS-NXD) as a Junior, which was one of the most degenerate formats ever (Mewtwo wars wheee) save for like Gym and a couple other WotC formats. At my first Regionals I played ZekEels, went up against Durant R1, and lost pretty badly, lol. The rest of it was a lot of fun, though.
That said, not long afterward, a bunch of friends of mine (most of whom had been playing since '08 or earlier) started to despair of Basic-dominated formats and build old decks from their favorite eras (and some from times before they started playing). Long story short, they got me into it, I started building old decks, and found old formats ridiculously fun. Most of my old decks right now are from DP-UL ('10) and MD-on (the first half of '11, before the emergency rotation), but I've also got a few from other formats (Base-Rocket, '05, '08, '12). I've also played a solid amount of other formats using friends' decks. I'd say my favorite would also have to be MD-on, like
@PokeMedic. It's just so diverse in terms of decks, techs, and strategies that there are a thousand different ways to play the format, and they're all awesome.
I think in general, people consider DP-on ('09 and '10) to be some of the best––if not
the best––formats the game has ever had. Games were intensely skill-based and could sometimes last an hour or so. Claydol GE, Uxie LA, and Broken Time-Space all existing in the same format allowed people to do insane things that in pretty much any other format would've been impossible. A friend of mine had this '09 Flygon list at one point that ran four Stage 2 lines––Flygon RR, Nidoqueen RR, Dusknoir DP, and Machamp SF––and he totally got away with it because the draw support in that era just made the deck consistent enough to work.