This is a question I get a lot actually. Because if you bring people who didn't grow up watching baseball to a game, their first impression is usually, "this is boring". And that's because it is boring. So why do Americans love it so much? Besides the simple reason that it has history and culture on its side (that you grow up learning to watch and play baseball), I'm going to include here a phenomenon I've noticed (again it's a generalization, comments welcome) that might shed some light on this question.
The thing that I've noticed is that if I rank American sports based on popularity (not including nascar), it'd go something like this (again feel free to disagree):
5 Ice hockey/Soccer
Now, I'm going to throw out golf and hockey and focus on the team sports. My theory is that Americans prefer discreteness in their sports compared to continuousness (yes this is a word, I looked it up). Ice hockey and soccer are the most continuous of the sports on that list. The clock doesn't ever really stop in soccer while substitutions are made continuously in hockey. Basketball has a continuous flow back and forth, but each possession is limited by the shot clock. Football is separated into every down of every drive of every possession. Each point in the game can be modeled by time, down, position on field, score, etc. to determine the next course of action. Then there's baseball, where every pitch of every at-bat of every inning is separate, and baseball is the most individual of the team sports.
This leads to my belief that Americans love the game of baseball and not the sport of baseball. There is usually more athletic ability on display in the more continous sports, and those tend to be more popular around the world (rugby, soccer, hockey, basketball, etc.). But baseball (and American football) offers more climactic moments for a fan because of the discreteness of plays. For example, there's a lot of buildup and cheering when a football team is trying to complete a crucial 3rd down. But nothing beats standing up and cheering on as the batter has two strikes on him with men on base and two outs with the pitcher looking to get out of the inning. And when the ball is fouled off, we get to sit down then stand back up and do it all over again. So my belief is that there are more dramatic situations in baseball and that's a large part of its popularity.
Another thing to look at from the discreteness of plays is the buildup of the score. In basketball, soccer, and hockey, a goal is a goal. There may have been a complicated process (pick and roll, passes, set play designs, faceoffs, etc.), but most will just remember the shot that scored the goal. While that also happens in football and baseball (one big play or a home run), there's also the 13 play drive in football or the bunt/stolen base/infield hit scenarios in baseball that build up to that score and make it seem more exciting.
So yes, to me, baseball is a boring sport and I rarely watch a regular season game even if I have a monetary interest in it. But I love watching the big games in late September and October when there's just so much drama built up into it.