Types

Dress and casual
Dress shoes are characterized by smooth and supple leather uppers, leather soles, and narrow sleek figure. Casual shoes are characterized by sturdy leather uppers, non-leather outsoles, and wide profile.
Some designs of dress shoes can be worn by either gender. The majority of dress shoes have an upper covering, commonly made of leather, enclosing most of the lower foot, but not covering the ankles. This upper part of the shoe is often made without apertures or openings, but may also be made with openings or even itself consist of a series of straps, e.g. an open toe featured in women's shoes. Shoes with uppers made high to cover the ankles are also available; a shoe with the upper rising above the ankle is usually considered a boot but certain styles may be referred to as high-topped shoes or high-tops. Usually, a high-topped shoe is secured by laces or zippers, although some styles have elastic inserts to ease slipping the shoe on.

Men's
This male dress shoe, known as a blucher, is distinguished by its open lacing.
Men's shoes can be categorized by how they are closed:
Oxfords (also referred as "Balmorals"): the vamp has a V-shaped slit to which the laces are attached; also known as "closed lacing". The word "Oxford" is sometimes used by American clothing companies to market shoes that are not Balmorals, such as Blüchers.
Blüchers (American), Derbys (British): the laces are tied to two pieces of leather independently attached to the vamp; also known as "open lacing" and is a step down in dressiness.
Monk-straps: a buckle and strap instead of lacing
Slip-ons: There are no lacings or fastenings. The popular loafers are part of this category, as well as less popular styles, such as elastic-sided shoes.
Men's shoes can also be decorated in various ways:
Plain-toes: have a sleek appearance and no extra decorations on the vamp.
Cap-toes: has an extra layer of leather that "caps" the toe. This is possibly the most popular decoration.
Brogues (American: wing-tips): The toe of the shoe is covered with a perforated panel, the wing-tip, which extends down either side of the shoe. Brogues can be found in both balmoral and blucher styles, but are considered slightly less formal.

Women's
There is a large variety of shoes available for women, in addition to most of the men's styles being more accepted as unisex. Some broad categories are:
High-heeled footwear is footwear that raises the heels, typically 2 inches (5 cm) or more above the toes, commonly worn by women for formal occasions or social outings. Variants include kitten heels (typically 1½-2 inches high) and stilletto heels (with a very narrow heel post) and wedge heels (with a wedge-shaped sole rather than a heel post).
Sneaker boot or sneaker pump: a shoe that looks like an athletic shoe, but is equipped with a heel, making it a kind of novelty dress shoe.
Mules are shoes or slippers with no fitting around the heel (i.e. they are backless)
Slingbacks are shoes which are secured by a strap behind the heel, rather than over the top of the foot.
Ballet flats, known in the UK as ballerinas, ballet pumps or skimmers, are shoes with a very low heel and a relatively short vamp, exposing much of the instep. They are popular for warm-weather wear, and may be seen as more comfortable than shoes with a higher heel.
Court shoes, known in the US as pumps, are typically high-heeled, slip-on dress shoes.

Unisex
Clog
Platform shoe: shoe with very thick soles and heels
Moccasin: originated by Native Americans, a soft shoe without a heel and usually made of leather.
Sandals: open shoes consisting of a sole and various straps, leaving much of the foot exposed to air. They are thus popular for warm-weather wear, because they let the foot be cooler than a closed-toed shoe would.
Espadrilles are casual flat warm-weather shoes of a style which originated in the Pyrenees. They usually have a cotton or canvas upper and a flexible sole of rope or rubber. There are high-heeled versions for women.
Saddle shoe: leather shoe with a contrasting saddle-shaped band over the instep, typically white uppers with black "saddle".
Slip-on shoe: a dress or casual shoe without laces; often with tassels, buckles, or coin-holders (penny loafers).
Boat shoes, also known as "deck shoes": similar to a loafer, but more casual. Laces are usually simple leather with no frills. Typically made of leather and featuring a soft white sole to avoid marring or scratching a boat deck. The first boat shoe was invented in 1935 by Paul Sperry.
Boots: Long shoes (covering the ankle) frequently made of leather. Some are designed to be used in times of bad weather, or simply as an alternate style of casual or dress wear. Styles include rubber boots and snow boots, as well as work boots and hiking boots.
Slippers: For indoor use, commonly worn with pajamas.
Vibram FiveFingers, meant to simulate the "natural" experience of going barefoot, while protecting the foot
Sneakers or Canvas shoes

Athletic
Men's and women's athletic shoes and special function shoes often have less difference between the sexes than in dress shoes. In many cases these shoes can be worn by either sex. Emphasis tends to be more on function than style.
Running shoes: very similar to above, with additional emphasis on cushioning.
Track spikes: lightweight; often with plastic or metal cleats
Cleat (shoe): a type of shoe featuring molded or removable studs. Usually worn while playing sports such as rugby, football, American football, or baseball.
Golf shoes: with "spikes" for better grip in grass and wet ground. Originally the spikes or "cleats" were made of metal but replaceable "soft spikes" made of synthetic plastic-like materials with prongs distributed radially around the edge of each spike are much more common today (and are required on many golf courses since they cause less damage to the greens).
Bowling shoes: intermediate style between ordinary dress shoes and athletic shoes. They have harder rubber soles/heels so as not to damage bowling alley floors. They are often rented or loaned at bowling alleys.
Climbing shoes: a shoe designed for rock climbing. They typically have a close fit, little if any padding, and a smooth sticky rubber sole with an extended rubber rand.
Hiking shoes or boots: usually have a high somewhat stiff upper with many lace eyelets, to provide ankle support on uneven terrain, with extra large traction on the sole.
Walking shoes: have a more flexible sole than the running shoe, lighter in weight than the hiking boot, may have air holes, may not be water proof.
Skating shoes: typically called skates. They have various attachments for skating on the bottom of the shoe portion.
Ice skates
Roller skates
Inline skates
Ski boot: a large, thick plastic boot specially designed for attachment to the ski.
Skate shoes: specifically designed for use in Skateboarding, the shoes are manufactured with flat soles as to allow a skateboarder to have better grip when riding a skateboard. They are very wide and have extra layers of padding to protect the skateboarders feet.
Cycling shoes are equipped with a metal or plastic cleat to interface with clipless pedals, as well as a stiff sole to maximize power transfer and support the foot.
Snowshoes are special shoes for walking in thick snow. In temperate climates, snowshoes are used for mostly recreational purposes in winter.
Wrestling shoes are light, flexible shoes that mimic bare feet while providing additional traction and protection.

Orthopedic
Orthopedic or "comfort" shoes are made with pedorthic and anatomically-correct comfort qualities, such as padded removable footbeds, wide toe boxes and arch support are made especially for those with problematic feet.

Dance
Pointe shoes are designed for ballet dancing. These have a toe box that is stiffened with glue and a hardened sole so the dancer can stand on the tips of their toes. They are secured by elastic straps and ribbons that are tied to the dancer's ankles.
Ballet shoes are soft, highly pliable shoes made of canvas or leather, with either continuous or two-part sole (also called split-sole). The sole is typically made of leather, with thicker material under the ball and heel of the foot, and thinner and thus more flexible material under the arch so that the foot can be pointed to its utmost. Ballet slippers are usually secured by elastics that cross over the top of the foot. They are most commonly pink, white, black, or pale tan, although they may be made in specialty colours such as red or blue.
Ghillies are soft shoes that are used in Irish dance, Scottish country dance, and highland dance.
Jazz shoes typically have a two-part, rubberized sole (also called split-sole) to provide both flexibility and traction, and a low (one inch or shorter) heel. They are secured to the foot by laces or elastic inserts.
Tango and Flamenco shoes are used for dancing the tango or flamenco.
Ballroom shoes fall into two categories: Ballroom and Latin American. Both are characterised by suede soles. Men's ballroom shoes are typically lace-ups with one-inch heels and patent leather uppers. Ladies' ballroom shoes are typically court shoes with two-inch heels, made of fabric that can be colored to match the dancer's dress. In contrast to the low Ballroom heel, which evenly distributes weight across the foot, Latin American shoes have higher heels designed to shift weight onto the toes. Latin shoes are also more flexible than ballroom shoes. Men's Latin shoes typically have 1.5- to 2-inch high, shaped heels, while Ladies' Latin shoes have 2,5-inch to 3-inch heels. Ladies shoes are typically open-toed and strapped.
Dance sneakers. Also known as dansneakers, these are a combination of a sneaker and a dance shoe, with a reinforced rubber toe.
Character shoes have a one to three inch heel, which is usually made of leather, and often have one or more straps across the instep to secure it to the foot. They may come in soft-soled (suede) or hard-soled varieties. They may be converted to tap shoes by attaching taps.
Foot thongs are known by various names depending on the manufacturer, including dance paws, foot undies, and foot paws. They are slip-on, partial foot covers that protect the ball of a dancer's foot from skin abrasions while executing turns. From a distance, flesh colored foot thongs give a dancer the appearance of having bare feet.
Tap shoes have metal plates mounted to the bottoms of the toe and heel. The metal plates, which are known as taps, make a loud sound when struck against a hard performance surface. Tap shoes, which are used in tap dancing, may be made from any style of shoe to which taps can be attached.

Work
Work shoes are designed to stand heavy wear, to protect the wearer, and provide high traction. They are generally made from sturdy leather uppers and non-leather outsoles. Sometimes they are used for uniforms or comfort by nurses, waitresses, police, military personnel, etc. They are commonly used for protection in industrial settings, construction, mining, and other workplaces. Protective features may include steel-tipped toes and soles or ankle guards.

Minimalist
Minimalist shoes are shoes that are minimal in design so that the advantages of walking/running barefoot are incorporated, yet without dropping additional protection of the foot from sharp objects, ... Minimalist shoes include: Vibram FiveFingers, MBT, Nike Free

Historical
Shoes of the past include:
Turn-shoes: a method by which the shoe is constructed inside-out, wetted, and turned — the finished side of the leather flipped to the outside. Such footwear was common from the Middle-ages until modern shoes were developed in the Tudor era. Because of their construction, turn-shoes cannot simply be re-soled, unlike most modern shoe types.
Espadrilles: these sandals, which are still worn today, are found as early as the 14th century.
Patten: a European wooden overshoe used to keep a person's feet dry outdoors. First worn in the middle ages, they continued in use even into the early 20th century. Peoples such as the Dutch, Flemings, and some French carved similar, fully enclosed wooden shoes.
Poulaine: a shoe with a long-pointed toe, popular in Europe in the 15th century.
Moccasins: the historical shoe of many North American Indian tribes.

Collection
Athletic sneaker collection has existed as a part of urban subculture in the United States for several decades. Recent decades have seen this trend spread to European nations such as the Czech Republic. A Sneakerhead is a person who owns multiple pairs of shoes as a form of collection and fashion. A contributor to the growth of sneaker collecting is the continued worldwide popularity of the Air Jordan line of sneakers designed by Nike for Basketball star Michael Jordan.

Source: Wikipedia