I would like to confirm I'm having exactly the same issue:
Basicly, when I "quit" clementine (by rightclicking the indicator icon and hitting "quit", not just using the close button), the process will remain active, and will keep doing whatever it was doing in the background.
Sometimes the cpu load will simply jump to 25-150% (don't ask me where that 150% comes from... "top" acting strange), and of course, that won't change by "quitting" the application.
Worse yet: start clementine again, and it'll spawn a new process instead of using the existing one! That second process can be extremely cpu-consuming as well.
(@nitstorm 's comment) There is nothing on the interface indicating that clementine is doing anything in the background.
Now I found a solution to this problem: according to http://code.google.com/p/clementine-player/issues/detail?id=2088 , it looks like it's a bug due to compatibility issues between clementine and the nvidia drivers.
One of the bug reports has posted the following command:
Exec=env __GL_NO_DSO_FINALIZER=1 clementine
I can confirm after a few tests, the above command fixes the issue.
To make life easier in ubuntu, you can change the clementine command in the menu editor.
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EDIT: In the menu editor, it seems you can't just use the command, so I made a script like this:
#!/bin/bash
Exec=env __GL_NO_DSO_FINALIZER=1 clementine
Saved as clementine.sh (don't forget to "chmod 755" the script to make it executable), and linked the Clementine menu entry to this script instead of the default command.
Works like a charm now, even when started from the dash instead of the launcher (if you have clementine set as default for music).