The best replacement for mapserver is geoserver.

The best alternatives to mapserver are rated as following:
★★★★★  geoserver
★★★  arcgis server
★★★  mapnik
★★★  mapguide
★  arcims
★  featureserver
★  arcgis
★  openlayers
  qgis server

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

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



Google Trends

Scale is based on the average worldwide traffic of mapserver in all years. Click on graph for more.
mapserver
geoserver
arcgis server