From guest editor Allison:
While counter stools with backs are not as glamorous as their swivel bar-stool cousins, they are an essential item for households with children. Perhaps this is why so many are reminiscent of schoolhouse furniture, a feature we find particularly appealing. Below are a few options that are as stylish as they are sensible.
MIDCENTURY MODERN CLASSICS

Above: Case Study Dowel Counter Stool (also available in a 30-inch height) is $475 at Modernica.

Above: High Chair K65 by Alvar Aalto for Artek; $475 at Unica Home.

Above: The Bertoia Counter Stool at DWR is $818 (currently 15 percent off, with free shipping).

Above: The Cherner Molded Plywood Counter Stool is $659 at Hive Modern.

Above: The Artek High Chair 617 is reminiscent of Jens Risom's work; made of birch with a choice of natural, black, blue, white, brown, or red webbing; $945 at Unica Home.
INDUSTRIAL RETRO

Above: Emeco Navy Stool; $650 to $725 (depending on finish and height) at Design Public.

Above: The Lyon Workspace Stool is a reliable workshop basic; $78.23 at CSN Chairs.

Above: The Haute Tabouret Tolix is available from Loft Butik for €269. The Tabouret Stool with a Short Back is available in the US through Melissa Edelman Antiquaire, a Chicago-area dealer who represents the full line of Tolix industrial chairs, stools, tables, and lockers in an array of custom colors. The 29.5-inch stool is $420 for a painted finish and $450 for raw steel in a matte or shiny finish.

Above: Stainless-steel Precision Stool with Backrest; on sale for $595 (down from $700) at Design Within Reach.
WOOD CLASSICS

Above: Director's Bar Stool; $59 at Home Decorators Collection.

Above: Ikea's Ingemar counter stool is $54.99.

Above: Homestead Bar Stool; $119 at Home Decorators.

Above: Blu Dot Timber Stool; available in graphite gray stain, natural beech, or ivory lacquer and as a counter or bar stool; $299 at Design Public.