The best replacement for squares is rectangles.

The best alternatives to squares are rated as following:
★★★★★  rectangles
★★★★  bars
★★★  bars recipes
★★★  see the stars
★★★  tiles
★★★  circles
★★  drapes
★  chips
★  cocoa powder
★  maximum likelihood
★  square roots
★  triangles
★  stars
★  chocolate chips
★  square meters
★  sharps
  bundles
  least circles
  sod rolls
  square metres
  prefolds
  square meteres
  linear regression
  stripes
  ordinary least squares

Your alternative for squares is not listed? Suggest!
Speaking about squares, one probably shouldn't forget about concentric circles.

Other search terms related to squares and their ratings are:
★★★★★ concentric circles
You have in mind a companion for squares and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of squares in all years. Click on graph for more.
squares
rectangles
bars