How come songs that I download play in quicktime instead of in iTunes?

There are several methods to set itunes as the default.

Using iTunes:
-Open iTunes.
-From the Edit menu, choose Preferences.
-Click the Advanced button and then click the General tab.
-Click “Use iTunes as the default player for all audio files” to select this option

or

-If you right click on the song you want to play you should have an option to open with.
-Then select “choose default program”
-In the new window that pops up you should have the option to select quicktime, itunes, or any other media player installed.
-Select the media player you want to use, in your case itunes.
-Then press ok. This should set all your music files in the same format to open in itunes.

If you have further questions please let me know.