The type of window you need is closely related to what you hope to achieve with your replacement project. Here are some pros and cons of various window types of some of the manufacturers that we work with.
STYLES

Awning Awning: A window that is hinged at the top and locks at the bottom.  (Think of an "awning". )  The window always pushes out. Ideal for maximum ventilation in a small opening.
Bay Window Bay window: 3 mulled windows, either at a 90, 45 (most common) or 30 degree angle. Comes (or must be built) with a headboard and seat board made out of wood.  Recessed lights can be installed in the ceiling of the bay. As this protrudes from the house a roof must always be constructed.  Sometime confused with a garden window.
Bow windowBow window: Like a bay window except it has 4 - 6 windows.
Casement window Casement window

Single: Hinged on the side and swings out.  Normal MAX Width is 36" wide.  Best on narrower width windows where you need maximum ventilation.  More expensive than other types of windows.

Double HungDouble Hung: Both the top and the bottom move vertically. Many newer designs will tilt in for ease of cleaning. MAX Width = 48".  Good if you want the top to open for ventilation, such as in a bathroom.
Double SliderDouble Slider: A horizontally sliding window with a vent on either side of a fixed panel of glass.
French Door French Door: An entry door where one or both sides swing inward or swing outward.
French Rail DoorFrench Rail Door: A horizontally sliding patio door with rails or styles which looks like a French door.
Garden WindowGarden Window: A 90 degree shaped window normally with a glass front, glass top, and 2 operable windows (normally single-hung) on either side. Commonly found in kitchens (maybe bathrooms) and used for plants. If heat from the sun is a problem this is not a good window.  Sometimes confused with a bay window.
HopperHopper: The least common window.  The window is hinged at the bottom and locks at the top. It is always pulled into the room. (Think of a "Hopper" or a shute".)  Most typically used in a high position where a pole must be used to open and close.
Horizontal SliderHorizontal Slider: The window slides horizontally with one moving part and one stationary panel.  Ideal when the width is wider than the height is tall.
Mulled windowMulled window: Two or more windows that are directly joined together side by side.  For example: 2 double hung windows side by side, both operating independently.
Picture WindowPicture Window: Fixed, doesn't open. MAX SIZE = 50 Sq Ft. (Windows over 40 square feet may not be available in all material types.)
Single-HungSingle-Hung: Looks like a double hung but only the bottom goes up and down.  The top is fixed.  Max Width = 48".  Cheaper than a double hung. Good if you never open the top such as in a kitchen over a sink.
Patio DoorPatio Door: A horizontally sliding door. Can be 2, 3 or 4 panels.