The font used for YouTube's logo is Trade Gothic Bold which is a grotesque sans serif font designed by Jackson Burke and published by Linotype. Here's the download link.

The first cuts of Trade Gothic were designed by Jackson Burke in 1948. He continued to work on further weights and styles until 1960 while he was director of type development for Mergenthaler-Linotype in the USA.

Trade Gothic does not display as much unifying family structure as other popular sans-serif font families, but this dissonance adds a bit of earthy naturalism to its appeal. Trade Gothic is often seen in advertising and multimedia in combination with roman text fonts, and the condensed versions are popular in the newspaper industry for headlines.