The best game I ever watched was at a MLB stadium (Dodger Stadium) even though it was not a MLB game. It was actually a 2009 World Baseball Classic game--the championship between Japan and South Korea. The stadium was packed though the stadium was consistently packed at that time during a regular season Dodgers game...well, except for the 7th inning when many of the fans and probably even a few of the players would leave early to beat the traffic.
What made this experience different though was the energy in the crowd. Dodger Stadium is pretty close to Koreatown and there also just happens to be an abundance of Korean-American and Japanese-American residents in the Los Angeles area. Most of the crowd was there to support South Korea, but there was also a fair number there to support Japan and the atmosphere was nothing like a MLB game (even a playoff game). It was more like a big time college football game. The stadium was loud and every pitch was treated like two outs at the bottom of the ninth in Game 7 of the World Series.
The fans for both teams were so passionate about the game that I think they would have brought that same energy regardless if the game was a close one or a blowout. Luckily, it was a great game. It went to extra innings and it just had to be that the biggest star in the game (the future Hall of Famer Ichiro Suzuki) would deliver the game winning hit that would put the dagger in the hearts of so many fans there.
Growing up and both playing and watching a lot of baseball, I don't think I could have ever imagined being at a baseball game like that. But the inherent excitement of baseball itself (the anticipation of the pitch, the one-on-one matchups, the unpredictability of what happens when the bat connects with the ball) coupled with how the game has evolved from America's pastime to a truly international sport turned that game into a one-of-a-kind experience that I will never forget.