There are a vast number of Hindi songs on YouTube. A search for "Hindi songs" on YouTube returns more than 10 million results, as of June 2015, and both old and new Hindi songs can be found.
Many YouTube channels are dedicated to Hindi songs, and the numerous playlists are caetgorized based on genres such as melody, romantic, sad and more. The best place to find good quality Hindi video or audio songs is on the YouTube channels of music labels and production houses. Rajshri, T-Series, Tips Music, ErosNow and Yash Raj Films are the major labels and production houses with official channels on YouTube.