Does apt-get clean harm your system?

Does cleaning /var/cache/apt/archives by apt-get clean affect installed applications?

Is it that the .deb packages there are needed for applications to run properly?

No, apt-get clean will not harm your system. The .deb packages in /var/cache/apt/archives are used by the system to install software. But once the software is installed, these .deb packages are no longer needed. You will need these .deb files only while re-installing the software. In case you do not need to re-install, remove these .deb files using apt-get clean.

From the manpage of apt-get.

clean clears out the local repository of retrieved package files. It removes everything but the lock file from /var/cache/apt/archives/ and /var/cache/apt/archives/partial/. When APT is used as a dselect(1) method, clean is run automatically. Those who do not use dselect will likely want to run apt-get clean from time to time to free up disk space.

Note the emphasized line. You should run apt-get clean from time to time.

The answer is no, it does no harm, not at all.

Not at all.

When you install an application, apt downloads needed .deb file, and then extracts its data into your file system. The .deb file is, however, kept - so that, for example, in case you want to reinstall that application, the .deb file will have been already downloaded. That means you can safely clean that cache with apt-get clean and it will not do any harm to your system and neither for applications.

This way you can free some disk space.