As Tavish and others have said, baseball has so many nuances that no other sport has such that, if you watch and learn these nuances, the game opens up into an incredible experience. I think these nuances are why people refer to baseball as a thinking person's game and wveres' example is a great one.
I love sports and follow teams in all. But my passion is baseball. On any single pitch, the game can be decided, and a 2-1 pitch in the 1st can be as important, if not more, than the first pitch in the 9th. Not to mention, regardless of the score or the inning, as long as a team has an out remaining, they have a chance to win because of the lack of time limit - definitely not the case in any other sport.
Also, in baseball, players have such varied skills, but they are always forced to go up against players whose skills do not match well - something that rarely occurs in other sports. A great fastball pitcher can blow away a weak hitter in one AB, and then have to face a great FB hitter the next. However, you rarely see a C being guarded by a PG (that doesn't lead into an immediate double-team) or a LB trying to cover a WR. Yet, despite this, you still don't know who will "win" a given match-up due to the vagaries of hitting a round ball with a round bat (where even a 1/4 of an inch can mean the difference between pop-up and HR).
I could go on, but it won't matter if someone has closed their mind to the beauties of baseball. But, if you're open-minded, try watching a game and think along with the players/managers. Watch how the first pitch of an AB is used to set up later pitches or how a hitter will work a count to get into a situation where the pitcher is "forced" to throw a good pitch (and then watch as the pitcher still doesn't throw that pitch). Watch how a pitcher follows a high inside FB with a CB down and away or how, after several changeups on the outside of the plate, he hits the inside corner with a FB which the batter just watches go by for strike 3. Of course, if the batter is thinking along and guesses right, he might turn on that inside fastball or drive that down and away CB and completely screw up the pitcher's strategy. And that's just a single AB. We haven't even discussed how the presence of baserunners can change all of the above, as well as the score of the game, the skills of the pitcher and hitter as well as numerous other factors.
And this is also just the pitcher/batter interaction, which occurs hundreds of times in a single game. After that, start watching the game strategies and how, despite the score being the same, they can change pitch-to-pitch or how even when the score changes, team strategies can remain the same.
Lastly, what I love is that at the start of every game, you never know what you'll see and even the best team will lose to the worst team app. 1/3 of the time. In the NFL and NBA, if the best team plays the worst team 18 times, I doubt you'll see teams with records of 12-6 and 6-12 afterwards - yet that happens consistently in baseball.