QGIS is a free software package for OS X, Windows and Linux that can manipulate and geographic information (e.g. shapefiles).
Leaflet is an easy-to-use JavaScript mapping library. We used to use Leaflet a lot in our programs, but have since mostly moved to MapBox GL JS.
MapBox GL JS is a JavaScript mapping library from MapBox. It uses WebGL to render maps, which basically means “you can put a lot more stuff on the map than you could with Leaflet.”
CARTO is a cloud-based mapping suite that allows you to work your data into attractive custom maps.