Here are some commonly used web & mobile mapping APIs;
GPSVisualizer - My old standby. Free, simple to use & modify (best in class!)
Leaflet - An Open Source JavaScript Library for Mobile Friendly Interactive Maps
Mapbox - An open source mapping platform for custom designed
maps. Their APIs and SDKs are the building blocks to integrate location
into any mobile or web app
CartoDB - Cloud Based Solution for your dynamic data, not free
ArcGIS - The Autocad of GIS programs. Widely used for the most sophisticated apps out there
Google Earth - The Google Earth plug-in allows you to navigate and explore geographic data on a 3D globe
using a web browser
WhirlyGlobe - Is a native iPhone Android API which displays a dynamic globe for your location data. Very Cool!