During the 2006 season, mlblogs.com started running a few player blogs, in addition to the regular Player Perspectives and other fun things running on mlbplayers.com.
And it's even more common in Japan for players to reach out to their fans by having a personal website and writing a blog. Some of them even write almost daily and in fairly good detail about games and players and random stuff.
If I listed all of the player blogs I read semi-regularly on the sidebar on Marinerds, I'd run out of space, and some of them are inactive, too, so I figured I'd list one or two of them there and then keep a page here of the rest.
Updated slightly less often: