Other than small ads that came a couple years later after youtube's first launch and paid videos to be displayed as featured videos how can a site like youtube that has so many expenses profit? Where does the money come from?
As far as I'm aware, I don't think it is making a profit yet.
Google owns YouTube - and Google are 'quite' well-off, so that's where the money comes from. ;)
It will make a profit eventually, though even if it doesn't it's most likely a worthwhile investment from Google's point of view. Having control over a resource as large as YouTube is useful from a strategic standpoint.
Think Blu-Ray vs HD DVD. Sony made a loss on every single PS3. Why? Because they wanted to get a blu-ray player into as many homes as possible. That meant the blu-ray 'won' the battle and now Sony are raking it in as a result.
Youtube has tons of Ads and has a huge revenue. Not sure the revenue does cover all the cost.
Here is a more recent article on it:
Here is an article (a bit old) which says its close to be profitable: http://www.neowin.net/news/youtube-still-not-profitable-but-its-close