All on the Dreamliner, all on the same flight (UA 94 IAH-DEN):
January 2014: Mechanical issue delays flight by 1.5 hrs, then the ice storm @ IAH suspends all operations for about 1.5 hrs, then the de-icing takes nearly 2 hrs (we only had two 777's in front of us - IAH is just not equipped for that kind of weather
February and March 2014: Mechanical issues delayed the departure by 3.5 hrs.
In all three instances I was continuing on to UA 139, the DEN-NRT flight. I've learned to just go with the flow and that it's better safe than sorry; I'm certainly not going to get bent out of shape, nor stressed out about it. You should have received apology emails from UA and your choice of a discount off your next purchase or a lump sum of RDM's. I took the discounts as it can be a nice discount off my business class fares ex GUM to the U.S.