In short: I’ve just uninstalled Audacity 2.0.5 (Windows 7), but surprisingly it still works.
I installed Audacity 2.0.5 a year and a half ago (in C > Programs files (X86) > Audacity). Today, I clicked on the uninstall file that was in the Audacity folder, and got a message that it was uninstalled. However, the Audacity folder wasn’t deleted, and I still have many files in it, including Audacity.exe itself, and when I click it, it works!
How do I completely remove Audacity? (BTW, I want to install the newest version).
The new version (2.1.0) may be installed over the top of 2.0.5. Just make a note of the 2.0.5 installation folder and ensure that you install 2.1.0 into the same folder.
As there are a lot of updates between 2.0.5 and 2.1.0 I would highly recommend that you enable the option to “Reset Preferences” during the installation.
If Audacity was running when you uninstalled it, that is expected. If that happened you should have seen a message that some files could not be deleted but can be deleted manually.