I particularly like the timeline.

Feb 2005 - 3 co-founders start work on site (1 later leaves)
May 2005 - public preview of site
Nov 2005 - launch of site
Nov 2005 - Sequoia (a Venture Capitalist) invests $3.5m
Apr 2006 - Sequoia invests another $8m (think they own 30% of YouTube)
Oct 2006 - Sold to Google for $1.65 billion

For Google, this effectively just buys them market share in the video space by taking them to >50%. Being the clear leader is a much better starting point if you're trying to negotiate with content providers to provide their content online, or if you want to set up an advertising business around it.

We won't really know if it pays off financially for them for a few years. In the worst case scenario where YouTube never makes money, it would only take 1-2% off Google's value given Google's size ($130 bil market cap vs $1.65 bil acquisition price).