The best replacement for arcgis is mapinfo.

The best alternatives to arcgis are rated as following:
★★★★★  mapinfo
★★★★  google earth
★★★★  arcview
★★★★  arcmap
★★★★  qgis
★★★  grass
★★★  google maps
★★★  autocad map 3d
★★  geomedia
★★  mappoint
★★  global mapper
★★  google maps api
★  mapbox
★  arcgis server
★  arcinfo
★  manifold
★  geoserver
★  autocad map
  arcims
  grass gis
  mapinfo professional
  gis
  quantum gis
  arcview gis

Your alternative for arcgis is not listed? Suggest!
Speaking about arcgis, one probably shouldn't forget about postgis.

Other search terms related to arcgis and their ratings are:
★★★★★ postgis
bing maps
You have in mind a companion for arcgis and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of arcgis in all years. Click on graph for more.
arcgis
mapinfo
google earth