The best replacement for openlayers is leaflet.

The best alternatives to openlayers are rated as following:
★★★★★  leaflet
★★★★  openstreetmap
★★★★  mapstraction
★★★  geoext
★★★  arcgis javascript api
★★★  mapbox
★★  polymaps
★★  mapserver
★★  cloudmade
★  openlayers
★  mapnik
★  gmap
  geoserver

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

Other search terms related to openlayers and their ratings are:
★★★★★ openstreetmap
★★★★ mapserver
★★★★ geoserver
★★ bing maps
★★ wms
★ arcgis server
★ mapbox
★ leaflet
You have in mind a companion for openlayers and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of openlayers in all years. Click on graph for more.
openlayers
leaflet
openstreetmap