The problem definitely has nothing to do with connection speeds on the user's end. I have a very fast connection (20/10), and whenever I have these difficulties I tend to also have no problem streaming HD video from sites like vimeo.

I also don't get this problem across all videos, and it doesn't affect all problem videos equally. The video you linked, Doug, does load fine for me, but watching the buffering bar, I saw it zoom to about two minutes in, then sit there until the play marker got really close, then it zoomed a little further. So I'm having a slight issue with that video, but it's not resulting in delays. (btw, you did post that video to one of the video threads here, so I do remember it)

As a sample test, here's a video (I'm researching blenders) I was trying in vain to watch earlier. Make sure to put it in 480p mode. For me it freezes at ~36 seconds. If I leave it, it'll eventually load the whole thing, but it'll take an unreasonably long time.

What I've also noticed is that with certain problem videos, I can get it to scoot along and load the next bunch of video simply by alternating quality levels. It'll get stuck, I change the quality, and the buffer will shoot out like it should. Then it'll get stuck, I'll change the quality back up, and the buffer shoots out again.

Another weird example: I just tried loading up OK Go's "This Too Shall Pass" video at 1080p to see how high quality video is affected by this problem I'm running into. You would think that it simply wouldn't load, or would get stopped far more often. Instead, the buffer chugged along at a great pace and the video played seamlessly, but I can see that for some reason it just decided to stop completely at 3:17 in the video. Then after about 2 minutes, it advanced to 3:20, 2 minutes later the whole thing.

Youtube was flawless for me last year. It always worked at all quality levels, even those ridiculously high levels they announced a while back. I started having issues with it around the same time that Tom did, late last year. I suspect you're right Tom, that it's their edge servers. It makes sense that a video from OK Go would be more easily played than a blender comparison from Popular Science, so that's probably what I'm seeing, but I still had a problem with the video with 26 million hits...
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Matt