Audacity has built-in support for Nyquist effects on all operating systems. You can download additional Nyquist plug-ins, or create your own using the Nyquist programming language. Nyquist code can be conveniently tested using "Nyquist Prompt" under the Effect menu.
Audacity has built-in support for LV2 plug-ins, which are an extensible successor of LADSPA effects. LV2 plug-ins are mostly built for Linux, but Audacity supports LV2 on all operating systems. To install LV2 plug-ins, place them in the system LV2 location then use the Plug-ins Manager to enable the new plug-ins as in the plug-in installation instructions.
Audacity can load VST effects (but not VST instruments) on all operating systems.
Starting with Audacity 3.2, VST3 effects are also supported on all operating systems.
LADSPA is superseded by LV2. These plug-ins are mostly built for Linux, but some old LADSPA plugins are available via the Legacy Windows and Legacy Mac sections.
This site is only meant as a starting point for effects. There are many more plugins, particularly VST3 ones, available on various vendor sites, directories and online stores. Some of them are listed below: