About 120. I can't catch the weekday day games due to work, and sometimes not at home during the weekends. I'll go back and watch parts of a few games or highlight plays or innings on MLB.TV.
And when I say I watch about 120, there are different levels of interest in watching games. I'll tune in and out during a game, do some other things for a bit. But you've never seen anyone move faster to the TV than me when I hear the sound of cheers and I'm not in front of the TV.
I box score or game day every game if I can't watch. I'll check my phone for scores pretty much every five minutes. I also follow the game threads when not watching, it tells a good story of what is happening.