On the boring side, I admit that I often fall asleep during the TV coverage of the middle of the stage. Phil & Paul's droning voices, plus the standard race strategy (an early break takes off with nobody significant in it, the pack lets them go, then the Yellow Jersey or sprinter's teams start hauling it in at a rate of 1 minute per 10 km, day after day), plus it's just a bunch of guys pedaling bikes.
But it really is quite interesting when you can look beneath all that and see what's really going on. The five races within the race (this would be the competitions for the four jersey classifications plus the competition for the stage win). Seeing if anyone is having a bad day. Trying to figure out why someone is attacking at a certain time or place, or why one of the teams is rapidly accelerating. Watching plans not work or backfire (Sagan trying to bridge up to the break on the descent before the intermediate sprints and failing, or Cadel's beautifully set up break with Tejay, only to get gapped by TVG once the attack is made. The climbing stages are always interesting, as guys attack and other guys go off the back.
But I do think that the coverage on the flat stages could be reduced considerably, focusing on the intermediate sprint and the final 20 km to the bunch sprint at the end. Phil & Paul also get it wrong quite often, regarding what's going on. I find ex-US-based pro Scott Moninger's comments to be far more perceptive, but it does helpl to listen to the analysis to get a better understanding of what's happening; this gives a much greater appreciation and thereby less boredom.
The live reports on Velonews, where a number of knowledgeable guys are commenting on the action as it happens, is also a good source (much better than the rather static live reports on cyclingnews.com).
Like anything else, the more background knowledge you have, the more interesting it gets. But yeah, I still fall asleep during the long, flat sections where nothing is happening!
Luis