I did some more digging since others are having the same problem. I found that if I disable "Identity Lock" the same youtube videos that won't run start running fine. Not all youtube videos are blocked, just certain ones for some reason. Here's one that is blocked consistently:
So, now I've found two settings within ZoneAlarm that cause some videos to hang, "Web Scan" and "Identity Lock". (for Identity Lock, go to the "Identity & Data" tab, choose settings for "Identity Protection", then set Identity Lock to "Off")
When I disable Identity Lock and leave Web Scan on, the video plays fine, and vice-versa. That tells me there is a problem with running both "Web Scan" and "Identity Lock" at the same time.
I tried adding youtube.com to the trusted sites and that did not change anything. I also tried both the Medium and High settings, both of which caused the video to hang. I've also had similar problems running videos on both ESPN and Yahoo.