Adhesive - the adhesive bra comes in two types, the paperless disposable bra, and the silicone type. The adhesive bra does not have any straps or bands and it adheres directly to the breast. It provides little in the way of support but can enhance the size and shape of the breast. The adhesive bra is particularly useful when wearing a backless dress.

Bandeau - the bandeau bra consists simply of a band of cloth that goes right around the body over the breast area. The bandeau bra is not designed to provide support or shape, simply coverage. It is a popular form of bikini top.

Balconette - the balconette bra is a 1930's invention that was designed to lift the breasts to enhance shape. It became popular during the 1950's.

Bralette - the bralette is a pullover type bra that is usually unlined and unwired. It is normally used by teens as a training bra.

Bullet - the bullet bra is a bra that has cups in the shape of the tip of a bullet. They are usually worn such that the breasts are pushed out perpendicular to the body. The bullet bra is normally associated with outlandish costumes with decorations to enhance shape, such as concentric circles radiating out from the nipples.

Convertible - the convertible bra has detachable straps and bands that can be arranged in different configurations so that the same bra can be worn with different sorts of clothes, such as strapless and backless dresses.

Cupless - the cupless bra is designed exactly as it sounds, and has no cups. Usually worn as exotic lingerie, the cupless bra provides very little support, but can sometimes enhance the nipples beneath other garments.

Front Closure - the vast majority of bras have fasteners on the straps worn at the back. As the name suggests, the front closure bra fastens at the front. This has the advantage of making the strap at the back almost flat against the body, making the bra less visible beneath tight fitting clothing.

Full Support - this is the typical kind of bra worn by fuller breasted ladies as every day under garments. They offer maximum support for ultimate comfort throughout the day. Mastectomy - these bras are specially designed to hold in place a breast prosthesis for women who for one reason or another may have lost one or both breasts.

Maternity - maternity bra is a wonderful invention for mothers who are breast feeding their children. The maternity bra's cups can expand over time to accommodate growing breasts during pregnancy and the cups themselves can be unfastened allowing access to the breast for feeding.

Minimiser - this type of bra is designed for larger women who may want their breasts to appear smaller. The bra compresses and shapes the breast into a more compact shape.

Padded - this is one of the best improvements to the bra since its invention. The padded bra has compartments built into the cups that house cloth or foam pads. The compartments can be below, around or over the breast area to enhance shape in different ways. Where women used to push things inside their bras such as tissue paper or other material in order to give the appearance of a larger breast, with the advent of the padded bra, this was now no longer necessary.

Plunge - the design of this bra, as the name suggests is such that the line plunges down between the breasts meaning that it can be worn with even the lowest of necklines. Because of its shape, the plunge bra, when worn with a low cut dress or t-shirt can enhance the appearance of the breasts.

Posture - again, this is a bra that does what it says in the name. The posture bra is structured in such a way as to help the wearer have a better posture.

Push Up - the push up bra is designed to lift and push together the breasts. This gives the impression of an enhanced cleavage, which again is sometimes desirable when wearing a low cut dress or t-shirt.

Racerback - the racerback bra has straps that come down the back in a V shape and the straps themselves are therefore much closer to the neck than traditional bras. The advantage is that the straps will not show when wearing sleeveless tops and dresses. The racerback design is also popular for sports bras as the placement of the straps provides more support meaning less bounce when running for example.

Sheer- this type of bra is made from fabric which is translucent and therefore allows the breast to be seen through the bra.

Shelf - the shelf bra again does what it says by having a rigid band which fits under the bra thereby pushing the breasts upwards. They also only have half cups so the nipple and most of the breast area is exposed and therefore gives the impression that the breasts have been placed on a shelf.

Softcup - the softcup bra has no underwiring or other type of rigidity to it. It simply relies on the strength of the material itself to support the breasts.

Sports - the sports bra is specially designed for active women and provides maximum support for the breasts to prevent them from bouncing during exercise, which can be painful, especially for larger breasted women.

Strapless - this type of bra has no shoulder straps and so is particularly useful when wearing clothing that reveals the shoulders of the wearer.

T-Shirt - the idea of the t-shirt bra is that it has no raised seems hand tend to have fasteners that do not cause the straps to be raised which means they can be almost invisible when worn beneath a t-shirt or other tight fitting item of clothing. T-shirt bras will also sometimes have a small amount of padding in order to prevent the shape of the nipple from being seen.

Training - these bras are designed for girls who are starting to develop breasts. They offer little or no support and are really only designed to allow girls to get used to wearing a bra.

Underwire - an underwire bra has a metal or plastic band or wire running within the fabric underneath the breasts. This allows the bra to give much more support to the breasts than relying on just the fabric itself.

Water and Gel Bras - this design of bra is essentially an evolution of the push up bra in that it has compartments in the bra cups that contain padding, but rather than the padding being made from cotton or other material as in the push up bra, the compartments have pads that are filled with silicone or water. Because this substance is less rigid it allows the breast to move around more freely so that the breast is enhanced but remains more natural looking.     

Bras/Types of Bras.  

Concise list of bra types and definitions/defining features purpose, along with images to demonstrate shape and design. Although this is not the entire list of bra models and makes, this list covers the vast majority and qualities held by the styles.(Definitions sourced from the Wikipedia 'List of brassieres' page...because I live dangerously...) 

 The adhesive bra, sometimes called a "stick-on bra" or a pair of "pasties", adheres to the breasts, often with one piece for each breast. There are no straps or bands of any sort. Provides little support to the breasts. Usually intended for backless and strapless fashions. There are two types: disposable paper bras that use a strong adhesive, and re-usable ones that use silicone and can be washed and re-used.  The balconette bra is a design that lifts the woman's breasts. First designed in the United States in about 1938, and came into mainstream fashion in the 1950s.  The bullet bra is a type of full-support bra with cups in the shape of a paraboloid of revolution with its axis perpendicular to the breast. The bullet bra usually features concentric circles of decorative stitching centred on the nipples. Invented in the late-1940s, they were still being sold well into the 1980s. The convertible bra has straps that may be detached and rearranged in different ways depending on the outfit. Alternatives to regular straps for strapless bras are beaded bra-straps or clear plastic bra-straps that provide support to the woman's bosom. The cupless bra, also called an open cup bra, or sometimes a shelf bra (see Shelf bra below), consist of a bra frame with no breast support or limited cups that only support a small portion of the lower half of the breast. Usually worn as erotic lingerie, a cupless bra can cause the shape of the nipples to be prominently visible beneath an outer garment. The demibra, also known as balconette bras, are a half-cup bra style with wide-set straps and a horizontal bust line. Often being seamed or boned, these promote cleavage and a bra-like effect. These offer less support but enable low-cut garments to be worn without the woman's bra being seen. Demibras can be designed to provide lift as do push-up bras. The front-closure bra: a bras that has closures, usually hooks and eyes, on its front rather than at its back. These bras lie almost completely flat at the woman's back. Some of these bras feature a racerback-style back (see below). The full support bra is a type of bra that is designed to offer good support for the entire breasts and, this is a typical, practical bra for everyday wear by a full-busted woman. The mastectomy bra is designed such that a breast prostheses is held in place, and these are intended for women who have lost one or both breasts by either mastectomy surgery for breast cancer or women who have been severely injured in a breast, such as by a gunshot wound or a traffic accident. The maternity bra is designed such that its cups do expand to adjust as the breasts' increase in size over the course of a pregnancy. The term "maternity bra" can also refer to a nursing bra. The minimizer bra is designed to de-emphasize the woman's bosom, in particular that of a large-breasted woman (size 32C and above). The minimizer bra, by compressing and shaping both breasts, helps to create the impression that a woman has a smaller bosom. The padded bra is simply a bra with cloth or plastic foam padding inside its lining, around, over, or below the woman's breast. This bra is designed to give a fuller shape for a small-bosomed woman. Of course, this bra is an alternative to stuffing the bra with paper tissues, socks, cotton balls, sugar packets, plastic foam, etc. Unlike push-up bras, most padded bras support the woman's breasts, but they do not significantly lift them. The plunge bra is generally worn with a low-cut blouse, dress, or sweater. (This can also be the design of a bikini top). As suggested by its name, this bra plunges down between the woman's two breasts. This allows the bra to remain covered by even a low neckline. In general, a bra that is exposed under a low-cut shirt worn in public is considered to be unfashionable and possibly even mildly distasteful by many people. In addition to remaining invisible under low necklines, the plunge bra will create and accentuate the line of the breasts. The posture bra is bra that is designed to help reinforce correct spinal posture and alignment. The push-up bra is structured so that the woman's breasts are lifted and placed closer together for cleavage enhancement by the woman. During the last few decades the best-known brand of push-up bra is the Wonderbra. Many push-up bras contain padding, typically made of foam or rubber, but some contain gel-filled pads. The main distinction between padded bras and push-up bras that incorporate padding is whether the padding is centered under the breasts to lift them or is outside the center so that the padding pushes the breasts inward. The racerback bra has shoulder straps that come over the shoulder in a "V" pattern very close to the neck. This design is sometimes worn under dresses or tops where "traditional" straps would be exposed. Many sports bras use racerback construction because this design is effective in providing good support to the breasts so that they do not bounce around very much.
   The sports bra provides firm support for both breasts, it is meant to prevent discomfort and stretching/sagging of the breasts during exercise times. Some women prefer to wear a sports bras exclusively, or even while sleeping. The strapless bra, which has no shoulder straps, is designed for women wearing clothing that reveals her shoulders, collarbone area, and perhaps the top halves of the breasts—as far low as the tops of the areola. This bra is good for wearing beneath strapless evening gowns by women who choose not to go braless. Training bras are designed for girls who have begun to develop breasts but for whom a standard-size bra does not fit properly. They are of simple construction and offer little, if any, support, but may aid in concealing developing nipples and breast buds and helping young girls grow used to putting on and wearing brassieres. The T-shirt bra is designed without any raised seams, hooks, etc., so that they fit against the wearer's skin smoothly, allowing the wearer to don a tight T-shirt, sweater, or sweatshirt with minimal bra visibility. These bras sometimes include a small amount of padding in their cups in order to conceal the nipples. Underwire bras are designed to give extra support and endurance. They have a wire (metal or plastic) running under each cup to provide rigid support to the bust. U-plunge bras are designed to be worn with a deep décolleté or plunging neckline.