Available Window Styles
Below you'll find a list of common window types.  These are not the only styles available. 
There are plenty of other options when you consider "mulling" windows together. 
Mulling is the act of joining two or more windows together to form one unit.
Common mulled units include two or three double hungs, a picture window
over an awning, two or more awnings stacked vertically, etc.
 

Double Hung	By far the most popular window on the market.  Both sashes slide up and down in a double hung, and only the bottom sash slides up and down in a single hung.  Double hungs have the option of a half or full screen on the outside.  Today's modern versions have tilt-in sashes for easy cleaning of the outside glass.  These all-around favorites do have some limitations; for example, they're not the best choice in locations where you have to stretch to open them, such as over a kitchen sink.  They generally have a higher air leakage rate than hinged windows.  Ventilation can vary from a small crack to almost half the total glass area.
Casement (Single, Double, Triple, Quadruple)	Casement windows are hinged on either the left or right side and swing outward. Hinged windows generally have lower air leakage rates than sliding windows from the same manufacturer because the operating sash closes by pressing a seal tight against the frame.  Casement windows provide significantly better ventilation than sliders of equal size.  Because the sash protrudes from the plane of the wall, it can be controlled to catch passing breezes, but screens must be placed on the interior side of the window.  Virtually the entire casement window can be opened, while sliders are limited to less than half of the window area.  They can be a poor choice where they would open onto patios or other traffic areas.  A casement window is operated by a crank and can make for a good window in a hard to reach place, such as over the kitchen sink.
Slider (Single / Double / Triple)	Sliders function like a double hung turned sideways.  Only one sash slides horizontally in a single-slider unit.  Both sashes slide in a double-slider.  In a triple slider, typically the middle pane is fixed in place and the two ends slide open for ventilation.  Sliders generally have a higher air leakage rate than hinged windows.  Ventilation can vary from a small crack to almost half the total glass area.  They look best in contemporary homes, and work well when opening onto a deck or exterior stairway, where a casement's swing would cause problems.
Awning	Awning windows are hinged at the top and swing outward.  Hinged windows generally have lower air leakage rates than sliding windows from the same manufacturer because the operating sash closes by pressing a seal tight against the frame.  Similar to casements, the entire window area can be opened, while sliders are limited to less than half of the window area.  They're often used for ventilation under large, fixed-pane picture windows in contemporary-style homes.  They keep out rain even when opened, as long as the wind isn't blowing too hard.
Hopper	Hopper windows are hinged at the bottom and open inward.  They are much like an awning in reverse.  Hinged windows generally have lower air leakage rates than sliding windows from the same manufacturer because the operating sash closes by pressing a seal tight against the frame.  Similar to awnings, the entire window area can be opened, while sliders are limited to less than half of the window area.  Hoppers are often used in basements where a window might not be able to swing outward.
Fixed	Fixed windows don't swing, tilt, or slide; the sash is permanently fixed to the frame.  They are often flanked by double hungs or casements in large openings, or set above or below an awning window.  Fixed windows are the most efficient window on the market, as they're permanently sealed shut and do not operate.
Bay	Bay windows will introduce more natural light into your home, expand your view of the outdoors, and actually make your room feel larger.  Bay windows can have either double hungs or casements on the ends for ventilation, with a large fixed window in the center for a maximum view.  Depending on size, it's also possible to have double hungs in all 3 openings for maximum ventilation.  A bay window can be ordered in 10°, 15°, 30°, 45°, or in a 90° "box bay".
Bow	Bow windows will introduce more natural light into your home, expand your view of the outdoors, and actually make your room feel larger.  Bow windows are a combination of casements and fixed picture windows.  There are numerous configurations on which windows operate and which ones don't.  A bow window can be ordered in 10° or 15° four-window,  10° five-window, or 10° six-window configurations that project outward from the house.  Bow windows create a nice curved look to your home.