Today I realized, that all images, that are located in sites/default/files/fields may not be accessed anymote, neither are they shown in my articles nor may I see them in the browser (e.g. http://daniel-stein.com/node/210#). All I get is a 403 - no permission - error. The folder and the files within are all set to 744 (and I also tested 777). I have not found any permissions I could adjust and I am not sure when this started or what I changed in that moment. Maybe it was around the time I changed from buedit to ckedit but the switch back was also useless.
Ok, so I found a solution that worked for me.
In the process of investigating in this problem and the fact why it does not appear on other Drupal installations I have running on the same server I messed up the permission settings on my server. In order to reorder things, I installed the module https://www.drupal.org/project/security_review - it produces a list with potential security problems of your Drupal installation. I worked myself down the list solving the issues one by one. I am not sure if this was the point in the beginning but after I changed the permissions of the .htaccess-file in sites/default/files to 444 (readonly) suddenly my images were accessible again.
For your reference, here are a lot of other approaches you can try if the one I presented is not helping: https://www.drupal.org/node/1170440