The first team I followed (although it was for only one year) was the Packers in '67, a pretty good season to discover pro sports. In '68 I moved to Georgia and decided to replace Bart Starr with Tommy Nobis. Plus, that had me set up for the '69 baseball season and the Braves who had a fantastic season ruined by the so-called "miracle mets", a disgusting group of perverts and ne'er-do-wells who couldn't carry Hank Aaron's jock strap. Ahem. Anyway...
Football was always on TV, baseball on the radio. I kind of lost interest in baseball when the Braves traded Aaron, and when I went in the Navy in '78,lack of regular TV access kind of ended my football fan days as well. Strangely enough, I rediscovered baseball in the Navy while serving as an ET on a ship homeported in Japan. I don't know what they do on ships now for entertainment, but back then, when you were out at sea you'd have video tapes of somewhat recent programs supplied and regularly replenished. Whenever I was the duty ET at sea, I had to show a few shows and then run a film (wish I'd never done that; to this day I can't ignore the 'change reels' warning...). Included were usually the baseball game of the week, and while I was forbidden to show them ("baseball is boring!"), I watched them myself and caught the bug again. I got out in '82 in time for the next great Braves season.
Like jeffcrom, the strike killed my baseball bug. I just didn't care anymore, and still don't. I'll occasionally read a book about baseball, but not often. In all honesty, I couldn't tell you right now who won the Series last year.