Online Mapping Apps
Google - My Maps - Simple, collaborative online mapping. Get Help here.
OpenStreetMap - Crowd-sourced data including physical features of all sorts, but no data analytics. What you can do in OpenStreetMap.
MapBox - The flexible mapping tool of choice for many big companies, but geared toward experienced developers.
Open-Source Software
QGIS -- This popular open-source GIS software runs on Linux, Unix, Mac OS, and Windows and supports numerous vector, raster, and database formats and functionalities. QGIS Learning Resources
gvSIG -- Rated by GISGeography.com as runner-up for ease of use as well as 3D capability, mobile apps, and CAD tools.