ArcGIS for Desktop from ESRI allows data to be shown on maps, but it also supports the management of data, analysis and the modelling and automation of workflows. There are many tools to support spatial analysis, and many data sources can be accommodated (more than 70 formats). Geographic, tabular, metadata and organisation tools are also provided. Creating maps is aided by wizards and templates, and a large library of symbols adds to the richness of the end result.
CartoDB is a geospatial database on the cloud that allows for the storage and visualization of data on the web. Using CartoDB allows rapid creation of map based visualizations. At its heart, CartoDB is an open source geospatial mapping Platform. It is a tool built to make mapping dynamic, scalable, and interesting. At its core, CartoDB is an Editor that gives a user friendly interface for making maps and visualizing data.
GeoCommons is the public community of GeoIQ users who are building an open repository of data and maps for the world. The GeoIQ platform includes a large number of features that allows users to easily access, visualize and analyze data. GeoIQ enterprise is the same platform that powers GeoCommons, but has additional features specifically geared for the enterprise. It includes intuitive analytics for insights and predicative capabilities. Social, local and mobile data can be used to see how they are impacting. ESRI now owns GeoIQ/Geocommons
Leaflet is designed with simplicity, performance and usability in mind. It works efficiently across all major desktop and mobile platforms out of the box, taking advantage of HTML5 and CSS3 on modern browsers while still being accessible on older ones. It can be extended with a huge amount of plugins, has a beautiful, easy to use and well-documented API and a simple, readable source code that is a joy to contribute to.
Mapbox Streets is a highly accurate worldwide map powered by up-to-the-minute data from the OpenStreetMap project. It’s built to be customized: change the map colors, show and hide features, and even configure the labeling language. Mapbox Terrain is a beautiful elevation and land-use layer for the entire world, visualizing hills and elevation contour lines. Terrain is just as easy to customize as streets – it’s simple to adjust color scheme or gently fade it for subtle map designs. Turn off labels and streets for a clean textured backdrop that makes custom cartography and data visualizations look beautiful. Mapbox Satellite offers highly-detailed imagery for the whole world. We process and color-correct millions of source images to create the best-looking up to date satellite layer available anywhere.
Modest Maps is a small, extensible, and free library for designers and developers who want to use interactive maps in their own projects. It provides a core set of features in a tight, clean package with plenty of hooks for additional functionality.
QGIS is a user friendly Open Source Geographic Information System (GIS) licensed under the GNU General Public License. QGIS is an official project of the Open Source Geospatial Foundation (OSGeo). It runs on Linux, Unix, Mac OSX, Windows and Android and supports numerous vector, raster, and database formats and functionalities.
You will find an excellent list of mapping tools and libraries here.