The sash window consists of two panels arranged vertically. This type of window is attributed to the English inventor Robert Hooke, its use caught on quickly due to the design's simplicity. In the single hung sash, the bottom panel moves up to allow the flow of air, while the top panel stays fixed.

The double panel sash window is probably the most widely used of all window types. It consists of two vertically arranged panels, both of which can be moved all the way up and down. 

The casement window was popular in the UK before the invention of the sash window and is still popular in many European countries. In this design, the operable panel (installed singly or in pairs) hangs on a hinge that enables the window to be opened like a door.

The awning window is a casement that's mounted vertically, with the hinge at the top so the window pushes out. This type of window is especially useful for allowing air to flow without admitting seasonal debris (e.g., falling leaves) or rainfall. 

Since their use in castles during the English Renaissance, bay windows have come a long way. Today—in mansions and modest homes alike—bay windows are beloved for allowing maximum light to enter a room, as the sun moves across the sky over the course of a day.

The bow window depends on a curved architecture and uses more glass panels than a bay window does (to account for the curvature). The window pictured is from the Hôtel Otlet in Brussels, Belgium.

The jalousie window is a distinctly American style, invented by Joseph W. Walker of Massachusetts in 1900. This type of window consists of thin, staggered strips of glass that open and close together like a Venetian blind.

The Palladian window is derived from the work of exalted Renaissance architect Andrea Palladio. The Palladian design is usually a large panel embellished by an arched top and two smaller side panels.

The sliding sash window consists of two horizontally mounted sashes that open and close easily by sliding along on a track. Sliders are an excellent choice of window to mount over a counter or sink—any circumstance where there is an obstacle to access. 

Fixed windows do not open; they can either be located on exterior walls to admit natural light or set into interior walls (e.g., over a door). This type of window comes in all sorts of shapes and sizes, and of course custom options are also available.