The format web maps speak - points, lines and polygons as plain JSON, with arbitrary properties hung off each feature. Leaflet, Mapbox and every mapping library read it natively, which makes it the usual destination for map data that came from somewhere else.
Every conversion below runs in this page, on your own machine. Nothing is uploaded, there is no queue, and there is no account to make. Pick a target format, or just drop a GeoJSON file above and choose afterwards.