Being a sports fan and a game designer, I can't help but want to modify the rules of the sports I follow. If I were made lord and master of MLB, these are the changes I would make to improve the game (in order of importance).
Eliminate the DH
The designated hitter is an abomination before god and man. It is fundamentally wrong and everything that is wrong with our current society can be directly traced to it. When you are old and grey, your grandkids will ask you what you did to stop the designated hitter rule. What will you tell them?
Automated Strike Calling
It's the 21st century. It is time for baseball to have a real strike zone that doesn't drift, shrink, or expand on the whim of an umpire. Having humans call balls and strikes just takes the game out of the hands of the players. That was necessary in the past, but not anymore (especially in the major leagues). Automated strike calling technology would now be very reliable and instantaneous. There is still plenty for the umpire to do (foul tips, base-running calls, check-swings, hit batters, controlling the pace of the game, etc.), so it's not like he's going away. The real objection is that this just isn't how baseball has traditionally been played. But if that bothers you, then wait until you read the next section.
3 Innings Instead of 9
I'm serious. Don't laugh, let me explain. The idea is to allow all nine players to bat in each inning, with the inning only being over once all nine are out (sort of like cricket). If your turn to bat comes up and you are on base, you are replaced by a pinch runner (who does not take your place in the lineup in this case), but if either you or one of your pinch runners (it's possible to have up to three at a time) is out, then you do not get to bat again in that inning (although you can still run the bases if the inning is not over). This change means there are only three innings instead of nine, of course.
Why do this? Because then you can't really pitch around the good batters, the game would go faster, and no team would ever be completely out of the game, regardless of the score. The end of each inning would be much more exciting as only the best batters would be left and a lot of the base runners would be super-fast base-stealing specialists (great base-running ability would be highly valued even if you aren't a great hitter). On-base percentage would become more important, tactics would change dramatically through the course of an inning, pitchers would be brought in (especially in the third inning) to get a specific batter out (not to pitch around him--to get him out in a high-stakes duel), and the top players would be more and more important (while still allowing minor players to have incredibly dramatic games).
I've run simulations of three-inning baseball, using average major league percentages, and the games generally aren't much longer. Measured by number of at-bats they would probably be about 5 at-bats longer per team, but the time of the game would generally be shorter because there would be so much less time wasted between innings. Scoring would be much higher (about 10 runs on average per team instead of 4), but I would consider this a good thing.
There are downsides, of course. You would have to throw away the record books (but is that really a problem in the steroids era?). A game that has a big nostalgia appeal would be very different (although the skills and individual plays wouldn't change at all). But if baseball has to do something dramatic to compete with football and basketball, this would do it. Also, this could be tested extensively in the minor leagues to see how well it worked before bringing it to the majors.