It's funny. I used to get a kick out of spring training, because it meant baseball and summer were on the way. Even though my team, the White Sox, usually sucked, I always associated baseball with summer, a great time of the year. And part of the charm of fall was postseason baseball, even if my team wasn't involved. It was fun to watch the best in the game square off.
Even in the 1990s, when I was in my 20s and literally didn't own a TV for several years, I would find my way into a sports bar or visit friends to watch the MLB playoffs. I distinctly remember the cool moment of Joe Carter's home run sailing out of the stadium as people went crazy in the Airliner, an Iowa City bar.
Fast forward to the 2010s (and now 2020), and baseball's no longer part of my leisure time. Haven't attended a MLB game since 2010, never watch games on TV, and rarely tune in on the radio any more (if so, it's just as background noise).
It takes an effort for me to watch even the MLB playoffs — in large part because I don't have cable TV, and I'll be damned if I pay those parasites at MLB.TV one dime of my money. The only playoffs on "free" TV are the World Series, and between the length of games and not following the season/playoff series much, the interest just isn't there.
So to answer the question: After football season ends, I follow college basketball through the NCAA tournament, and watch the majors in golf and (occasionally) tennis. That's it anymore.