Try cp -n option. It will copy but will not overwrite. The man page of cp says:
-n, --no-clobber
do not overwrite an existing file (overrides a previous -i option)
Example:
$ cp -n -R * destination_folder
-R is for recursive copy.
-R, -r, --recursive
copy directories recursively
If you want to do it interactively, you can use -i
-i, --interactive
prompt before overwrite (overrides a previous -n option)