You can find a list of A to Z song titles at AZLyrics.com as of 2015. The site has a comprehensive list of songs from across the world along with the lyrics.
You can search for songs on AZLyrics.com by finding the artist, or you can type a song name into the search bar. Each artist or band on the site's directory has a subsection that lists all of their albums and shows which songs were in the albums.
The homepage of AZLyrics.com identifies currently popular songs with its "What's Hot" section, while more information can be found about the site on its Facebook page.