As recommended I have installed the TeXnicCenter 2 beta 1 over my TeXnicCenter RC 1 installation.
In principle it works quite well, but if I try to open my templates (TeXnicCenter/Templates) clicking File/New/File from Template... it is not displayed correctly. There only appear squares. This indeed seems to indicate an encoding problem. But if I call the same (!) file using File/Open/File... it is displayed correctly (it can also be compiled without any problems).
In summary: The same (!) file is displayed correctly by TeXnicCenter 2 beta 1 if opened "normally" via File/Open/File..., whereas it is buggy via File/New/File from Template...
In TeXnicCenter RC 1 this error does not occur.
@Kurt: Path: C:\Programme\TeXnicCenter\Templates\Documents\Deutsch. Filename: It happens with every template, regardless of the filename (one example: Standard.tex). Encoding: I normally use ANSI or UTF-8. In the present case: If the file is opened normally via File/Open/File... TeXnicCenter says it is UTF-8 encoded; if opened via File/New/File from Template... TeXnicCenter says it is UTF-16 encoded. This seems to be the problem, but I have no idea why TeXnicCenter uses UTF-16 if the file is opened via File/New/File from Template... and I do not know how to fix that.
It appears that I am at least not the only one having this problem, see this report on sourceforge.net
MikTeX 2.9, Windows XP.