You asked "Do I have to keep all the old versions...". Of course not. You can do whatever you want. Each version of LabVIEW installs in its own directory, which is what allows you to keep multiple versions installed in case you need to support programs written in earlier version that cannot be upgraded yet for whatever reason. Conflicts may arise if you install older versions later than new ones and you install the libraries for the hardware interfaces like VISA and such. Older versions of these libraries sometimes cause problems with newer versions of LabVIEW.
If you do not want multiple versions, common practice is to completely uninstall the current version before installing the new one. If you have more than two versions but only want the latest, simply uninstall the older ones from the main NI installer. Depending on how old the versions are that you are uninstalling something with the new one may break so you may need to repair that installation. You may just want to simply uninstall all NI software and then just do a clean install of the latest version. That will likely be your best course of action.
