The best replacement for shapefile is geodatabase.

The best alternatives to shapefile are rated as following:
★★★★★  geodatabase
★★★  coverage
★★★  layer
★★★  feature class
★  layer file
★  personal geodatabase
  shapefile

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

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



Google Trends

Scale is based on the average worldwide traffic of shapefile in all years. Click on graph for more.
shapefile
geodatabase
coverage