Strangely, in no less than three of the anime I’ve watched within the past week, there have been featured characters swinging baseball bats (this doesn’t include the sweaty anorexic characters of One-Outs). In Kurokami it was simply being used (poorly I might add) as a weapon, but in the other two there was a deeper meaning than just using it to hit a ball or bash the heads of residents of Hinamizawa. I’ve always seen swinging a bat as somewhat more threatening than swinging a sword. Whereas a sword is razor sharp and will slice you into ribbons at the drop of a hat, a bat will smash, mash and crush; it’s a brutal and inferior weapon and in the right hands is meant to injure and cause suffering rather than kill.
But of course in these other two shows that wasn’t what the action represented. The swinging of a bat is a focusing device. It represented the determination of the character in either achieving or forgetting something. To lose yourself in a repetitive excercise and forget your troubles, or to use that same exercise to demonstrate your resoluteness and conviction; never did I realise how great a metaphor swinging a bat is.
Grand Punk Railroad 
What was the third one? I’ve only seen it in Kurokami and Clannad. Although I might be completely forgetting something that I watched.
If you’re going to take it that far, it’s not limited to just swinging a bat. In that case, you could use running, swimming, any repetitive exercise really. In fact, I’d say running is more of a demonstration of resoluteness. It’s just one long march, while swinging a bat is more of a repetitive burst activity. You swing, then you stop, rinse and repeat. Running is constant. Same could be said of swimming and I’m sure there’s more activities like that.
If my memory serves me correctly, Al Capone famously used a baseball bat to personally execute a competitor, but that might be a myth I picked up somewhere. It’s a sporting object that can become a weapon at the drop of a hat.
(I tried to come up with a segue to shift my comment on to the cricket bat in Shaun of the Dead, but I couldn’t.)
@Nazarielle
I was just noting the trend I saw in anime previously, you could easily expand upon it. But then you could say it wasn’t even limited to anime, what about the abundance of excercising montages in almost evey sports movie ever made?
@The Animanachronism
If by baseball bat you mean chainsaw, then yes :P. I don;t know about that, but what I do know is that EVERYONE SHOULD JUST CALM THE F*CK DOWN <— couldn’t think of any other way to relate this comment to it either.