How can I backup my programs/applications, so that after I reinstall a new one, I can still use the backup-ed ones?

When I have to format my Ubuntu I follow this steps:

1. dpkg --get-selections > package_list This creates a text file (package_list) with all package installed in your system. You can edit the file if you want to delete some packages.
2. Backup /etc/apt/sources.list file and /etc/apt/sources.list.d/ folder. Here there are all the repositories.
3. Backup /home/MyUser folder. All application settings are hide folders/files in your user's home folder, maybe you want to select what settings you want to restore.
4. Format and install new Ubuntu.
5. Restore your repositories (/etc/apt/sources.list file and /etc/apt/sources.list.d/ folder).
6. sudo apt-get update && sudo apt-get upgrade
7. sudo dpkg --clear-selections and sudo dpkg --set-selections < package_list. To restore the information of your installed packages.
8. Install them: sudo apt-get update && sudo apt-get dselect-upgrade
9. Finally, sudo apt-get autoremove to clean some packages.

Well, there are 9 steps, but you have an easy Ubuntu clean install.

Another solution is to mantain a list with your installed applications, then sudo apt-get install app-name (you can create a bash script).