The best replacement for postgis is spatialite.

The best alternatives to postgis are rated as following:
★★★★★  spatialite
★★★★  oracle spatial
★  shapefile
  mysql spatial

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

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



Google Trends

Scale is based on the average worldwide traffic of postgis in all years. Click on graph for more.
postgis
spatialite
oracle spatial