I do. I'll start one, and than pause it to go do something else (write code, grab a snack, etc) and come back and start watching a different show. Eventually, I'll get distracted and pause the show I'm watching and talk on IRC or read Twitter for a bit, at which point I'll read about another show that I've been meaning to watch. So, I'll start watching it. Only to remember the first show that I started two hours ago and never finished. Its worse when I catch a reference to another show that I'm watching but can't quite remember what its referencing or its baseball season and I have a Mets game to watch..

This works really well with Quicktime, where it opens a new window for every video file I tell it to play. Not so much with VLC or Movist (mplayer UI) on OS X, that use a single window for all videos.