No, at least not in person.
DC Metro reports lower ridership numbers compared to 2013 and 2009. This is significant because DC metro is used heavily and with many streets closed for the inauguration, it's the primary means of transportation for those who want to attend.
The national park service retweeted a now infamous picture on twitter comparing the 2009 and 2017 crows which seems to show much smaller number of people for Trumps inauguration. The tweet has been deleted since.
Another thing to look at is the inauguration parade. Here is a video of the Obama parade and a video before the Trump parade.
In terms of "around the globe" - this article by Snopes, cites the Nielsen Company according to which 31 million Americans watched Trump's inauguration and thus ranks 5th in terms of TV viewership.
Obviously, the US is not the world, so it's possible that the viewership was higher in other countries thus making up the shortfall in US viewership, but that seems unlikely due to a number of reasons.
Crowd estimation is very subjective and could be controversial so this might be the best data we can get. I think it's fair to say this was probably not the largest inauguration crowd ever.