Can't play albums in iTunes I know you've been dealing with this for two years.  However, none of the recommended solutions works for me.  iTunes will play one song, and stop.  Or, it will play one song - over and over and over.  I am using iTunes vsn. 12.0.1, updated on 10/21/14, on a Mac running OS 10.7.5.
This is often caused by iTunes' insistence on only playing songs that are 'checked', even though you can't tell whether they're checked or not except in Songs view. 

If you don't need the functionality that checking songs is used for (syncing with other devices, or limiting what appears in smart playlists), you can turn it off by unchecking Preferences > General > Show List Checkboxes. Then iTunes will play any selection you like without stopping.

If you don't want to disable checkboxes, as @Buscar웃 says, the Up Next list is your (somewhat unintuitive) friend.