While it is impossible to know the exact number of people that watched the event at one time, Akamai, Limelight and Highwinds combined did over eight million simultaneous streams for Obama's inauguration video, across all of their customers. Limelight said they peaked at around 2.5 million streams, Highwinds say they saw about 625,000 and my estimate is that Akamai did around 5 million.
While Akamai put out a press release saying they did seven million simultaneous streams across their network, they did not break out how many of those were just for the inauguration. Since they peak at around a million streams already on any given day and the release states that some of the seven million streams were on demand, I figure Akamai did around five million simultaneous just for today's inauguration. (I have a call into Akamai asking for an explanation and will update the post when I hear back)
In addition, CDNs including Level 3 and others delivered some live streams of the event, but in much smaller numbers. Adding all of them up and I think a fair estimate would be that between 8-9 million people were all watching a live video stream at the same time.
Hard to know how this compares to other events since most of the CDNs don't give out simultaneous stream counts, but it's definitely up there in terms of being a large number across all of the CDNs combined.