Yes, you can listen to a lot of music midis found on the web if you have sound speakers and the right plug-ins such as "Real Player" or Media Player on your computer.

Cyberhymnal - see a listing of over 2600 hymns.  Select "Titles", then go to the next page for the alphabetical listing.  Select the "letter" for title of hymn.  A box will likely come up and you will hear the song and you should be able to READ the words.

Heavenly midis – Select from many different categories for selecting the songs.

Christian Book. com - Search for a song by Title and listen to sample midi for the music.  This site allows you to insert the name of a song that you have heard and then you can select the musicians and listen to the song before you purchase the soundtrack from a store. 

Classical Music -- Many composers from the Classical Era, including Bach, Beethoven, Handel, Tchaikovsky, Mendelssohn, Debussy, and others with hundreds of selections to chose from. (Membership now required to this website)

Click on the arrow to listen to a sample.

Example of Handel: "The Messiah"