In ArcGIS Python code:
CopyFeatures_management copies features to the same featureclass - that means overwrite to the feature class. How can I add new features to one featureclass or namely different featureclasses and prevent overwriting in the loop?
You are mistaken. CopyFeatures_Management copies features from the input feature class to a NEW (output) one. See the documentation here
So in your loop, use a variable name for the output feature class that gets changed each iteration to something suitable
[EDIT AS PER SYD'S REQUEST] Here's a very simple example. Suppose you are looping over a list of Feature Classes, just create a new name each loop:
Alternatively, did you mean "how do you do make a loop using model builder?"
NOTE: I have only roughed this out quickly. In ArcGIS 10 you can also use iterators in Model Builder which can sometimes allow you to have a list or series of inputs. I haven't got space here to describe how to set up all the iterators for every use-case by the ESRI documentation is helpful for this.
Are you looking to add the features from one feature class to an Existing feature class? If So, you need the Append Tool.