2004, of course, even though I can't really separate '03 and '04 in the sense that it was a constant psychodrama from Opening Day '03 straight through to 10/27/04. Even that offseason was more exciting than most regular seasons I can remember.
Regardless, that was the pinnacle and thank God we'll never have to go through something like that again.
That said, 1995 may have been the most purely enjoyable season I ever experienced. I became a fan when I was 5, in '77. I remember the Dent HR, being kind of bummed out that they got rid of the red hats, and pretty much all of my favorite players leaving over a three year span. I'd pretty much lost interest by the time Yaz retired and, other than playoffs and a very occasional trip to Fenway, don't think I consciously went out of my way to watch a game for the next ten years. I turned 21 in '93 and figured that a nice way to kill a summer night would be to spend it drinking beer in the bleachers. I got more than I bargained for in that as soon as I set foot into Fenway, I instantaneously fell in love with the whole thing all over again. From that night on, I was all-in. Of course, these were the Butch years and they were pretty much awful, though Mo, Val, Naehring, and Sele (not to mention DD at the helm) all boded well for the future. Finally, the strike ended and baseball was back... and for the first time in my adult life, I was watching a good Red Sox team. And for about a two and a half month stretch that summer, Wakefield was Pedro before there was a Pedro (even though Pedro was just starting to be Pedro up in Montreal... but that's not the point). It seemed that every time he took the mound, there was a very good chance he'd throw a no-no.
They were eventually killed off by Tony Pena, Infant Manny, and co., but it still felt so good to be rooting for a Sox team that was able to maintain a hot stretch for more than a week or so at a time. Granted, the residual good karma I felt evaporated quickly when they won, like, 5 games in April '96, but '95 was my first taste of success, I was grateful for it, and overall it was just a hell of a good time.